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CuCl etchant is progressing

CuCl etchant is progressing

2003-04-23 by grantfair2001

I am happy to say that I can now see unmistakeable signs of progress
with my etchant. I now have about 17 litres of it, in a 34 litre
Coleman cooler, gugrgling away on the floor next to my laundry tubs.

The air bubbler I made is the type described at Think & Tinker:

http://www.thinktink.com/stack/volumes/voliii/equipmnt/bubltank/bubltank.htm

I am using air from the exhaust output of a small vacuum pump.
Sometime recently, the bubbler started putting out more air, so almost
all the surface of the etchant is constantly bubbling vigorously. I
don't know whether the sparger moved, or the pump, which has carbon
vanes, suddenly decided to put more air out. The pump has been running
continuously for several days with only slight heat to the touch for
the motor case. The pump casing seems even less warm than the motor
casing.

Anyway, I can see two changes tonight (in addition to the more
vigorous air bubbling).

The etchant is an even deeper brown color than it has been for a few
days. It is so dark I can hardly see the wire under the etchant
surface. And all the remaining wire is clearly decreasing in diameter.
(I hung one piece of copper wire over the edge of the tank about 4
days ago. The etched part is 1/2 the diameter or less than the
unetched end). Also, at the start, the whole mass of copper wire was a
large jumble, with some wire under etchant and some above it. Clearly
the etchant is working, because the level of wire above the surface
has substantially decreased.

It is great to see this working, after the slow start I had, and all
my worrying and wondering. I hope I will be able to start etching
boards within a week or so. Yahoo!

I do like this process because:

1) it is non-polluting

2) replenishing HCl is cheap and easy to do

3) a Coleman cooler, 8 litres of HCl, and 5 pounds of copper wire,
along with a bubbler are all it took me to get started, (along with a
hell of a lot of advice)

4) this list is a great source of information and encouragement
(thanks Adam, and everyone else who helped!)

5) cheap and dirty chemical analysis is possible - see:

http://www.pacificsun.ca/~robert/pcb/pcb.htm

for related work by Donald Aitken and Robert Grauman

Grant

Re: [Homebrew_PCBs] CuCl etchant is progressing

2003-04-23 by Adam Seychell

I'm glad to see its finally working.
As I learned on the weekend, the bubbles is what makes the
process move forward. It was a bad idea to initially let the
copper stay in a stagnant solution. The correct method is to add
all the acid and copper together in one hit and bubble it like
crazy. Then wait until it turns to a transparent deep green. At
150g/L of copper (SG 1.3) you won't see through more than 1cm
without a bright backlight. A drop on white surface shows up nice
bright green.

Thanks for this link, http://www.pacificsun.ca/~robert/pcb/cucl.htm

I like his idea of HCl titrations using a eyedropper and counting
the drops. Just look for the formation of insoluble Cu hydroxide,
which will turn the solution cloudy. The eye dropper method is
good enough for determining the acid content of this etchant. An
indicator will make it easier. I'll post more analysis details
another time.

The HCl can be very low 0.1M and still etch perfectly ok. At very
high say 3M then it will create more fuming. The HCl should never
be zero because air regeneration cannot happen and your solution
will quickly build up insoluble copper(I) film over the copper
and inhibit etching.
One thing I noticed in the article is that he uses much lower
copper content (100g/L of CuO) or 80g/L of copper. I'm sure at
140g/l copper you get over double the speed, I'll have to check
that again.

Grant, you mention 5.0 pounds of copper (2.3kg). if you desire
140g/L of dissolved copper then you looking at 16 liters of
etchant !. Thats a lot of etchant :) Worry about disposal another
day.

The HCl will needed to react with all this copper and have some
left over for about a 1M of free HCl then you'll need;

Moles of copper = 2300grams / 63.5 = 36 moles

Cu + 2HCl -> CuCl2

So you need twice as many moles of HCl than moles of Cu, or 72
moles. You also need another 16 liters * 1 Mole/liter = 16 moles
of HCl. Total moles of HCl = 72+16 = 88.

according to.

http://www.starch.dk/isi/tables/hcl.htm

and the fact that molecular weight of HCl = 36.g grams/mole
then
30%wt HCl = 345g/l = 345/36.5 = 9.5 Moles/Liter.

then to calculate the volume HCl needed to get 88 moles

Total volume of 30% HCl = 88/9.5 = 9.3 liters.

I hope I'm making some sense here.

Adam





grantfair2001 wrote:
> I am happy to say that I can now see unmistakeable signs of progress
> with my etchant. I now have about 17 litres of it, in a 34 litre
> Coleman cooler, gugrgling away on the floor next to my laundry tubs.
>
> The air bubbler I made is the type described at Think & Tinker:
>
> http://www.thinktink.com/stack/volumes/voliii/equipmnt/bubltank/bubltank.htm
>
> I am using air from the exhaust output of a small vacuum pump.
> Sometime recently, the bubbler started putting out more air, so almost
> all the surface of the etchant is constantly bubbling vigorously. I
> don't know whether the sparger moved, or the pump, which has carbon
> vanes, suddenly decided to put more air out. The pump has been running
> continuously for several days with only slight heat to the touch for
> the motor case. The pump casing seems even less warm than the motor
> casing.
>
> Anyway, I can see two changes tonight (in addition to the more
> vigorous air bubbling).
>
> The etchant is an even deeper brown color than it has been for a few
> days. It is so dark I can hardly see the wire under the etchant
> surface. And all the remaining wire is clearly decreasing in diameter.
> (I hung one piece of copper wire over the edge of the tank about 4
> days ago. The etched part is 1/2 the diameter or less than the
> unetched end). Also, at the start, the whole mass of copper wire was a
> large jumble, with some wire under etchant and some above it. Clearly
> the etchant is working, because the level of wire above the surface
> has substantially decreased.
>
> It is great to see this working, after the slow start I had, and all
> my worrying and wondering. I hope I will be able to start etching
> boards within a week or so. Yahoo!
>
> I do like this process because:
>
> 1) it is non-polluting
>
> 2) replenishing HCl is cheap and easy to do
>
> 3) a Coleman cooler, 8 litres of HCl, and 5 pounds of copper wire,
> along with a bubbler are all it took me to get started, (along with a
> hell of a lot of advice)
>
> 4) this list is a great source of information and encouragement
> (thanks Adam, and everyone else who helped!)
>
> 5) cheap and dirty chemical analysis is possible - see:
>
> http://www.pacificsun.ca/~robert/pcb/pcb.htm
>
> for related work by Donald Aitken and Robert Grauman
>
> Grant
>
>
>
> Be sure to visit the group home and check for new Bookmarks and files:
> http://groups.yahoo.com/group/Homebrew_PCBs
>
> To unsubscribe from this group, send an email to:
> Homebrew_PCBs-unsubscribe@yahoogroups.com
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

Re: CuCl etchant is progressing

2003-04-30 by grantfair2001

Hi Adam -

Though I mention 5 pounds of copper in the related post, in fact I
used less. It was about 4 pounds, plus a bit more from an extra test
wire I hung over the side and a 3" x 5" piece if PCB I used to confirm
etching. My original etchant consisted of 4 litres of 31.5% (20
Beaume) HCl and 8 litres of distilled water. (I thought I was making
10% HCl but I think I needed a different formula). Later I added 500
ml of 3% hydrogen peroxide. Later yet I added about a cup of distilled
water. And later again I gradually added approximately 3 litres of
31.5% HCl. And, since the tank lid was off until the weekend, some of
the etchant may have evaporated - enought to rust some tools, anyway!

I think I need to study up on "stoichiometry". My highschool chemistry
was over 30 years ago, and I have forgotten all I ever knew, which
probably wasn't all that much.

I understand that your calculations below were in reply to my earlier
post. Maybe the above will make it easier for you to approximate any
adjustment I should now be making to the etchant. As I said in a
recent post, the ph has changed from 2 to 3 in the last day or so.

Grant

--- In Homebrew_PCBs@yahoogroups.com, Adam Seychell
<adam_seychell@y...> wrote:
> I'm glad to see its finally working.
> As I learned on the weekend, the bubbles is what makes the
> process move forward. It was a bad idea to initially let the
> copper stay in a stagnant solution. The correct method is to add
> all the acid and copper together in one hit and bubble it like
> crazy. Then wait until it turns to a transparent deep green. At
> 150g/L of copper (SG 1.3) you won't see through more than 1cm
> without a bright backlight. A drop on white surface shows up nice
> bright green.
>
> Thanks for this link, http://www.pacificsun.ca/~robert/pcb/cucl.htm
>
> I like his idea of HCl titrations using a eyedropper and counting
> the drops. Just look for the formation of insoluble Cu hydroxide,
> which will turn the solution cloudy. The eye dropper method is
> good enough for determining the acid content of this etchant. An
> indicator will make it easier. I'll post more analysis details
> another time.
>
> The HCl can be very low 0.1M and still etch perfectly ok. At very
> high say 3M then it will create more fuming. The HCl should never
> be zero because air regeneration cannot happen and your solution
> will quickly build up insoluble copper(I) film over the copper
> and inhibit etching.
> One thing I noticed in the article is that he uses much lower
> copper content (100g/L of CuO) or 80g/L of copper. I'm sure at
> 140g/l copper you get over double the speed, I'll have to check
> that again.
>
> Grant, you mention 5.0 pounds of copper (2.3kg). if you desire
> 140g/L of dissolved copper then you looking at 16 liters of
> etchant !. Thats a lot of etchant :) Worry about disposal another
> day.
>
> The HCl will needed to react with all this copper and have some
> left over for about a 1M of free HCl then you'll need;
>
> Moles of copper = 2300grams / 63.5 = 36 moles
>
> Cu + 2HCl -> CuCl2
>
> So you need twice as many moles of HCl than moles of Cu, or 72
> moles. You also need another 16 liters * 1 Mole/liter = 16 moles
> of HCl. Total moles of HCl = 72+16 = 88.
>
> according to.
>
> http://www.starch.dk/isi/tables/hcl.htm
>
> and the fact that molecular weight of HCl = 36.g grams/mole
> then
> 30%wt HCl = 345g/l = 345/36.5 = 9.5 Moles/Liter.
>
> then to calculate the volume HCl needed to get 88 moles
>
> Total volume of 30% HCl = 88/9.5 = 9.3 liters.
>
> I hope I'm making some sense here.
>
> Adam
>
>
>
>
>
> grantfair2001 wrote:
> > I am happy to say that I can now see unmistakeable signs of progress
> > with my etchant. I now have about 17 litres of it, in a 34 litre
> > Coleman cooler, gugrgling away on the floor next to my laundry tubs.
> >
> > The air bubbler I made is the type described at Think & Tinker:
> >
> >
http://www.thinktink.com/stack/volumes/voliii/equipmnt/bubltank/bubltank.htm
> >
> > I am using air from the exhaust output of a small vacuum pump.
> > Sometime recently, the bubbler started putting out more air, so almost
> > all the surface of the etchant is constantly bubbling vigorously. I
> > don't know whether the sparger moved, or the pump, which has carbon
> > vanes, suddenly decided to put more air out. The pump has been running
> > continuously for several days with only slight heat to the touch for
> > the motor case. The pump casing seems even less warm than the motor
> > casing.
> >
> > Anyway, I can see two changes tonight (in addition to the more
> > vigorous air bubbling).
> >
> > The etchant is an even deeper brown color than it has been for a few
> > days. It is so dark I can hardly see the wire under the etchant
> > surface. And all the remaining wire is clearly decreasing in diameter.
> > (I hung one piece of copper wire over the edge of the tank about 4
> > days ago. The etched part is 1/2 the diameter or less than the
> > unetched end). Also, at the start, the whole mass of copper wire was a
> > large jumble, with some wire under etchant and some above it. Clearly
> > the etchant is working, because the level of wire above the surface
> > has substantially decreased.
> >
> > It is great to see this working, after the slow start I had, and all
> > my worrying and wondering. I hope I will be able to start etching
> > boards within a week or so. Yahoo!
> >
> > I do like this process because:
> >
> > 1) it is non-polluting
> >
> > 2) replenishing HCl is cheap and easy to do
> >
> > 3) a Coleman cooler, 8 litres of HCl, and 5 pounds of copper wire,
> > along with a bubbler are all it took me to get started, (along with a
> > hell of a lot of advice)
> >
> > 4) this list is a great source of information and encouragement
> > (thanks Adam, and everyone else who helped!)
> >
> > 5) cheap and dirty chemical analysis is possible - see:
> >
> > http://www.pacificsun.ca/~robert/pcb/pcb.htm
> >
> > for related work by Donald Aitken and Robert Grauman
> >
> > Grant
> >
> >
> >
> > Be sure to visit the group home and check for new Bookmarks and files:
> > http://groups.yahoo.com/group/Homebrew_PCBs
> >
> > To unsubscribe from this group, send an email to:
> > Homebrew_PCBs-unsubscribe@yahoogroups.com
> >
> >
> >
> > Your use of Yahoo! Groups is subject to
http://docs.yahoo.com/info/terms/
> >
> >

Re: [Homebrew_PCBs] Re: CuCl etchant is progressing

2003-04-30 by adam Seychell

The etchant HCl and copper can very widely and work ok. Make
up the 1.0M standard NaOH solution by dissolving 40.0g of
NaOH in liter of water, store in polyethylene bottle. You
will need access to some scales +-1g or better. You should
only ever need to to this once. Then use the eye dropper
technique to get a rough estimate of free HCl.
You really need an pH indicator because I found that by
simply looking for copper hydroxide formation is very
difficult. The indicator must change color before about pH
4.0, because the copper chloride seems to hold the pH around
there while its converted to copper hydroxide.
I use methyl orange pH 3.1 ~ 4.4. Unfortunately phenol red
sold at pool stores changes at pH 6.8 ~ 8.4.
Maybe you can stick in pH paper and watch for a color
change. I found long list of indicators.
http://chemdat.merck.de/cdrl/services/labtools/en/table_abindic.html

It sounds like there is plenty of acid because you talk
about fumes and the fact a drop turns clear after some time.
I would of got more than one 12" air stone, or as many as
the pump can handle. You can leave the airstones in
permanently and have a second air hose specifically for
regeneration.


grantfair2001 wrote:
> Hi Adam -
>
> Though I mention 5 pounds of copper in the related post, in fact I
> used less. It was about 4 pounds, plus a bit more from an extra test
> wire I hung over the side and a 3" x 5" piece if PCB I used to confirm
> etching. My original etchant consisted of 4 litres of 31.5% (20
> Beaume) HCl and 8 litres of distilled water. (I thought I was making
> 10% HCl but I think I needed a different formula). Later I added 500
> ml of 3% hydrogen peroxide. Later yet I added about a cup of distilled
> water. And later again I gradually added approximately 3 litres of
> 31.5% HCl. And, since the tank lid was off until the weekend, some of
> the etchant may have evaporated - enought to rust some tools, anyway!
>
> I think I need to study up on "stoichiometry". My highschool chemistry
> was over 30 years ago, and I have forgotten all I ever knew, which
> probably wasn't all that much.
>
> I understand that your calculations below were in reply to my earlier
> post. Maybe the above will make it easier for you to approximate any
> adjustment I should now be making to the etchant. As I said in a
> recent post, the ph has changed from 2 to 3 in the last day or so.
>
> Grant
>
> --- In Homebrew_PCBs@yahoogroups.com, Adam Seychell
> <adam_seychell@y...> wrote:
>
>>I'm glad to see its finally working.
>>As I learned on the weekend, the bubbles is what makes the
>>process move forward. It was a bad idea to initially let the
>>copper stay in a stagnant solution. The correct method is to add
>>all the acid and copper together in one hit and bubble it like
>>crazy. Then wait until it turns to a transparent deep green. At
>>150g/L of copper (SG 1.3) you won't see through more than 1cm
>>without a bright backlight. A drop on white surface shows up nice
>>bright green.
>>
>>Thanks for this link, http://www.pacificsun.ca/~robert/pcb/cucl.htm
>>
>>I like his idea of HCl titrations using a eyedropper and counting
>>the drops. Just look for the formation of insoluble Cu hydroxide,
>>which will turn the solution cloudy. The eye dropper method is
>>good enough for determining the acid content of this etchant. An
>>indicator will make it easier. I'll post more analysis details
>>another time.
>>
>>The HCl can be very low 0.1M and still etch perfectly ok. At very
>>high say 3M then it will create more fuming. The HCl should never
>>be zero because air regeneration cannot happen and your solution
>>will quickly build up insoluble copper(I) film over the copper
>>and inhibit etching.
>>One thing I noticed in the article is that he uses much lower
>>copper content (100g/L of CuO) or 80g/L of copper. I'm sure at
>>140g/l copper you get over double the speed, I'll have to check
>>that again.
>>
>>Grant, you mention 5.0 pounds of copper (2.3kg). if you desire
>>140g/L of dissolved copper then you looking at 16 liters of
>>etchant !. Thats a lot of etchant :) Worry about disposal another
>>day.
>>
>>The HCl will needed to react with all this copper and have some
>>left over for about a 1M of free HCl then you'll need;
>>
>>Moles of copper = 2300grams / 63.5 = 36 moles
>>
>>Cu + 2HCl -> CuCl2
>>
>>So you need twice as many moles of HCl than moles of Cu, or 72
>>moles. You also need another 16 liters * 1 Mole/liter = 16 moles
>>of HCl. Total moles of HCl = 72+16 = 88.
>>
>>according to.
>>
>>http://www.starch.dk/isi/tables/hcl.htm
>>
>>and the fact that molecular weight of HCl = 36.g grams/mole
>>then
>>30%wt HCl = 345g/l = 345/36.5 = 9.5 Moles/Liter.
>>
>>then to calculate the volume HCl needed to get 88 moles
>>
>>Total volume of 30% HCl = 88/9.5 = 9.3 liters.
>>
>>I hope I'm making some sense here.
>>
>>Adam
>>
>>
>>
>>
>>
>>grantfair2001 wrote:
>>
>>>I am happy to say that I can now see unmistakeable signs of progress
>>>with my etchant. I now have about 17 litres of it, in a 34 litre
>>>Coleman cooler, gugrgling away on the floor next to my laundry tubs.
>>>
>>>The air bubbler I made is the type described at Think & Tinker:
>>>
>>>
>>
> http://www.thinktink.com/stack/volumes/voliii/equipmnt/bubltank/bubltank.htm
>
>>>I am using air from the exhaust output of a small vacuum pump.
>>>Sometime recently, the bubbler started putting out more air, so almost
>>>all the surface of the etchant is constantly bubbling vigorously. I
>>>don't know whether the sparger moved, or the pump, which has carbon
>>>vanes, suddenly decided to put more air out. The pump has been running
>>>continuously for several days with only slight heat to the touch for
>>>the motor case. The pump casing seems even less warm than the motor
>>>casing.
>>>
>>>Anyway, I can see two changes tonight (in addition to the more
>>>vigorous air bubbling).
>>>
>>>The etchant is an even deeper brown color than it has been for a few
>>>days. It is so dark I can hardly see the wire under the etchant
>>>surface. And all the remaining wire is clearly decreasing in diameter.
>>>(I hung one piece of copper wire over the edge of the tank about 4
>>>days ago. The etched part is 1/2 the diameter or less than the
>>>unetched end). Also, at the start, the whole mass of copper wire was a
>>>large jumble, with some wire under etchant and some above it. Clearly
>>>the etchant is working, because the level of wire above the surface
>>>has substantially decreased.
>>>
>>>It is great to see this working, after the slow start I had, and all
>>>my worrying and wondering. I hope I will be able to start etching
>>>boards within a week or so. Yahoo!
>>>
>>>I do like this process because:
>>>
>>>1) it is non-polluting
>>>
>>>2) replenishing HCl is cheap and easy to do
>>>
>>>3) a Coleman cooler, 8 litres of HCl, and 5 pounds of copper wire,
>>>along with a bubbler are all it took me to get started, (along with a
>>>hell of a lot of advice)
>>>
>>>4) this list is a great source of information and encouragement
>>>(thanks Adam, and everyone else who helped!)
>>>
>>>5) cheap and dirty chemical analysis is possible - see:
>>>
>>>http://www.pacificsun.ca/~robert/pcb/pcb.htm
>>>
>>>for related work by Donald Aitken and Robert Grauman
>>>
>>>Grant
>>>
>>>
>>>
>>>Be sure to visit the group home and check for new Bookmarks and files:
>>>http://groups.yahoo.com/group/Homebrew_PCBs
>>>
>>>To unsubscribe from this group, send an email to:
>>>Homebrew_PCBs-unsubscribe@yahoogroups.com
>>>
>>>
>>>
>>>Your use of Yahoo! Groups is subject to
>>
> http://docs.yahoo.com/info/terms/
>
>>>
>
>
>
> Be sure to visit the group home and check for new Bookmarks and files:
> http://groups.yahoo.com/group/Homebrew_PCBs
>
> To unsubscribe from this group, send an email to:
> Homebrew_PCBs-unsubscribe@yahoogroups.com
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

Re: CuCl etchant is progressing

2003-04-30 by grantfair2001

Thanks again, Adam-

I found an inexpensive balance made in India for C$15 and it is
remarkably sensitive, comparing the weights included against those of
Canadian coins, whose weight is listed by the mint on the web.

I also found an inexpensive source of indicators in the US who will
send them up here.

After 12 hours with the airstone I don't see any change in etchant
color. The ph was still at 3 today so I added the bit of HCl left in
the 4 litre jug. I will get more airstones as you suggest, and see
what happens.

Grant

--- In Homebrew_PCBs@yahoogroups.com, adam Seychell
<adam_seychell@y...> wrote:
> The etchant HCl and copper can very widely and work ok. Make
> up the 1.0M standard NaOH solution by dissolving 40.0g of
> NaOH in liter of water, store in polyethylene bottle. You
> will need access to some scales +-1g or better. You should
> only ever need to to this once. Then use the eye dropper
> technique to get a rough estimate of free HCl.
> You really need an pH indicator because I found that by
> simply looking for copper hydroxide formation is very
> difficult. The indicator must change color before about pH
> 4.0, because the copper chloride seems to hold the pH around
> there while its converted to copper hydroxide.
> I use methyl orange pH 3.1 ~ 4.4. Unfortunately phenol red
> sold at pool stores changes at pH 6.8 ~ 8.4.
> Maybe you can stick in pH paper and watch for a color
> change. I found long list of indicators.
> http://chemdat.merck.de/cdrl/services/labtools/en/table_abindic.html
>
> It sounds like there is plenty of acid because you talk
> about fumes and the fact a drop turns clear after some time.
> I would of got more than one 12" air stone, or as many as
> the pump can handle. You can leave the airstones in
> permanently and have a second air hose specifically for
> regeneration.

Re: [Homebrew_PCBs] Re: CuCl etchant is progressing

2003-05-01 by Adam Seychell

grantfair2001 wrote:
> Thanks again, Adam-
>
> I found an inexpensive balance made in India for C$15 and it is
> remarkably sensitive, comparing the weights included against those of
> Canadian coins, whose weight is listed by the mint on the web.


That's a good idea. I'm sure a new coin would be much better than
+-1% accurate.
If you are buying lab stuff get a eye dropper bottle (the ones
with the dropper fixed to a screw top lid) and also a normal eye
dropper. Make up 1 liter of about 0.002% pH indicator in clean
bottle using DI water. Put the standard 1.0 Molar NaOH solution
in the dropper bottle. Take 10 drops of etchant into a rinsed
glass (using the normal eye dropper), then add about 10 ~ 20 ml
of the pH indicator. Whilst stirring carefully add drop by drop
the 1.0M NaOH until color changes. Each drop represents 0.10M of
free acid in the etchant. Having separate dropper for each
solution means there is little to clean up. That should make acid
analysis a piece of cake.

If you have a burette then of course use that because its much
more accurate ?

>
> I also found an inexpensive source of indicators in the US who will
> send them up here.

What indicators are you getting ?

>
> After 12 hours with the airstone I don't see any change in etchant
> color. The ph was still at 3 today so I added the bit of HCl left in
> the 4 litre jug.

I would imagine the dark color of this solution would make pH
papers useless.

Re: CuCl etchant is progressing

2003-05-01 by grantfair2001

I was thinking of getting bromophenol blue and methyl orange. What do
you recomend? Shipping tends to be expensive so I thought I would try
to get everything I needed (or might) at one time.

The indicator paper showed a clear red color which corresponded to pH
2 and then pH 3. The etchant color did not seem to interfere.

Grant

--- In Homebrew_PCBs@yahoogroups.com, Adam Seychell
<adam_seychell@y...> wrote:

> > I also found an inexpensive source of indicators in the US who will
> > send them up here.
>
> What indicators are you getting ?
>

> I would imagine the dark color of this solution would make pH
> papers useless.