Molybdenum (Mo) is a heavy metal that can have severe health effects on humans and animals. Tailings from a mining operation in Colorado have polluted surface waters used by grazing animals with Mo. Based on the following information determine the concentration of the three Mo species in the stream. [Mo]T = 5.1x10^-4 M pH = 4.20

H2MoO4 (aq) = HMoO4^1- (aq) + H+ (aq) pKa1 = 4.0

HMoO4^1- (aq) = MoO4^2- (aq) + H+ (aq) pKa2=4.24

Are you in to mole fractons or alpha zero, alpha 1 and alpha 2?

Mole fractions

X(H2MoO4) = (H^+)^2/D

X(HMoO4^-) = k1(H^+)/D
X(MoO4^2-) = k1k2/D
where D is denominator and that =
(H^+)^2 + k1(H^+) + k1k2

when you finish calculating each mole fraction, then X*5.1E-4 = (that specie)

There is another way to do this without mole fractions. It's about as long to do it that way but it has the advantage of not using those formula I have above. If you've seen those derived you know where they come from.

To determine the concentration of the three Mo species in the stream, we need to consider the equilibrium between the species. Let's break down the problem step by step:

1. The primary species in the stream is H2MoO4 (aq), also known as molybdic acid. It can dissociate as follows:
H2MoO4 (aq) ⇌ HMoO4^1- (aq) + H+ (aq)

2. We are given the pKa1 value, which is the logarithm of the acid dissociation constant for the first equilibrium. We can use this value and the pH of the stream (pH = 4.20) to calculate the concentration of HMoO4^1- (aq) species.

pKa1 = -log(Ka1)
Ka1 = 10^(-pKa1)

Since the reaction is at equilibrium, we can assume that [H2MoO4] = [HMoO4^1-], and the concentrations of H2MoO4 (aq) and H+ (aq) can be neglected compared to the concentration of HMoO4^1- (aq).

[HMoO4^1- (aq)] = [H2MoO4 (aq)] = Ka1 / [H+]

[H+] can be calculated using the pH value:
[H+] = 10^(-pH)

Substituting the values, we can calculate the concentration of HMoO4^1- (aq).

3. The second equilibrium involves the species HMoO4^1- (aq) and MoO4^2- (aq):
HMoO4^1- (aq) ⇌ MoO4^2- (aq) + H+ (aq)

We are given the pKa2 value for this equilibrium. Similar to the previous step, we can use this value and the pH of the stream to calculate the concentration of MoO4^2- (aq) species.

[MoO4^2- (aq)] = [HMoO4^1- (aq)] / [H+] = [H2MoO4 (aq)] / ([H+]^2)

4. We are given the total concentration of molybdenum ([Mo]T = 5.1x10^-4 M). To determine the concentration of H2MoO4 (aq) species, we need to subtract the concentrations of HMoO4^1- (aq) and MoO4^2- (aq) from the total molybdenum concentration.

[H2MoO4 (aq)] = [Mo]T - [HMoO4^1- (aq)] - [MoO4^2- (aq)]

By following these steps and substituting the given values, you can determine the concentration of the three Mo species in the stream.