Optimal Metol/hydroquinone ratio

[River Mantis]

From Haist, p. 447

These authors [A. J. Axford and J. D. Kendall] found that the maximum rate of development for an MQ series of developers was obtained when the molar percentage of Metol was 28 %

There is also an old post where a graph from LFA Mason's book was posted showing the maximum rate at about 25-30%. The graph is labeled "Effect of the molar ratio of Metol to hydroquinone on developer activity" which is probably misleading. Just from the graph itself and the notion of the total concentration in centimoles per litre I assume that this is indeed a ratio of Metol to total quantity of two compounds.
So the weight ratio of Metol would be

X = K*r/(K*(r-1)+1) ~ 0.55
where
K = 0.28
r = MMetol/MHQ = 344.38/110.11

So the developer should have slightly more Metol by mass than HQ but in most formulas we have 3-6 times more HQ than Metol by mass. What am I missing?

 

[relistan]

From Haist, p. 447

There is also an old post where a graph from LFA Mason's book was posted showing the maximum rate at about 25-30%. The graph is labeled "Effect of the molar ratio of Metol to hydroquinone on developer activity" which is probably misleading. Just from the graph itself and the notion of the total concentration in centimoles per litre I assume that this is indeed a ratio of Metol to total quantity of two compounds.
So the weight ratio of Metol would be

X = K*r/(K*(r-1)+1) ~ 0.55
where
K = 0.28
r = MMetol/MHQ = 344.38/110.11

So the developer should have slightly more Metol by mass than HQ but in most formulas we have 3-6 times more HQ than Metol by mass. What am I missing?

Those tend to be reuseable developers where the HQ is getting exhausted by replenishing the metol (the primary dev agent), and it is used over multiple rolls of film. HQ does a little bit of development as well, but the main role there is usually just to support the metol. So the metol doesn't get used up until the HQ is pretty well gone. But that means you need more than the optimum ratio of HQ. If you were to use it one shot, you would be able to get away with a lot less HQ. Maybe at the exact ratio Mason quotes, or maybe needing slightly more to account for storage loss.

 

[Jimskelton]

I'm not sure there is an "optimal" Metol/HQ ratio for all situations. If you want a high contrast developer, Metol can be as low as 10% (Ansco 42). If you want a low contrast developer it can be as high as 100% (D-23, Ansco 120). Also factored in is the amount of activator (Sodium Carbonate/Borax, etc.) and restrainer, which all determine how "active" the developer ends up being.

 

[River Mantis]

I'm not sure there is an "optimal" Metol/HQ ratio for all situations. If you want a high contrast developer, Metol can be as low as 10% (Ansco 42). If you want a low contrast developer it can be as high as 100% (D-23, Ansco 120). Also factored in is the amount of activator (Sodium Carbonate/Borax, etc.) and restrainer, which all determine how "active" the developer ends up being.

Optimal in terms of a time of development to a specific gradient value like in sources mentioned above

 

[Alan Johnson]

The diagram that is linked in post 1 is on p119 of Photographic Processing Chemistry [1975 ed] by LFA Mason.
It refers to a pH of 10.6 ,cf about 8.6 for D-76/ID-11.
From p120 "For all organic agents , increase in pH results in increased activity.............being much greater in the lower alkalinity range (8-9.5)..........."
So in addition to the factors mentioned in posts above, you are missing that the diagram is for a pH not normally encountered in practice and assuming that the effect will be identical.
Maybe it will be, maybe not.

 

[Lachlan Young]

From the SPSE Handbook, the following suggested starting points:

At a pH of 9, it suggests a 1:2 M:Q ratio
At a pH >10 it suggests an M:Q ratio of 1:4-10