Question

The balanced redox reactions for the sequential reduction of vanadium are given below.
reduction from +5 to +4:
2 VO2+(aq) + 4 H +(aq) + Zn(s) → 2 VO2+(aq) + Zn2+(aq) + 2 H2O(l)
reduction from +4 to +3:
2 VO2+(aq) + Zn(s) + 4 H +(aq) → 2 V3+(aq) + Zn2+(aq) + 2 H2O(l)
reduction from +3 to +2:
2 V3+(aq) + Zn(s) → 2 V2+(aq) + Zn2+(aq)
If you had 10.5 mL of a 0.0036 M solution of VO2+(aq), how many grams of Zn metal would be required to completely reduce the vanadium?

Answer 1

So how many electrons do you need to completely reduce the vanadium ion presented above?

Answer 2

2?

Answer 3

You need 2 electrons at each individual step reaction, but the total amounts to 6 electrons. Now how many electrons can each Zn atom contribute (how many can it lose)?

Answer 4

3?

Answer 5

nope, each Zn atom can contribute 2 electrons (\(Zn^{2+}\) is most oxidized form that be achieved here)

So, if you need 6 electrons for each V ion, and you get 2 electrons from each Zn atom, you need 3 times as many right?

"If you had 10.5 mL of a 0.0036 M solution of VO2+(aq), how many grams of Zn metal would be required to completely reduce the vanadium?"

Now all we need to do is find the moles of V ion present, and multiply it by 3. This gives us the moles of Zn needed. Finally, we convert to moles of Zn to grams of Zn.

Answer 6

Okay so where do I need to start to find the moles of V ion present?

Answer 7

Look at the information given in the question, and specifically the units used.

"you had 10.5 mL of a 0.0036 M solution of VO2+(aq)"

What units of concentration are you given here?

Answer 8

mL so do I need to convert to grams?

Answer 9

You need to find the moles of V ion first.

Answer 10

Also, mL are not the units of concentration, M (Molarity) is the unit of concentration.

you need use the definition of molarity, \(\sf molarity=\dfrac{moles~of~solute}{L~of~solution}\)

Answer 11

Sorry I read over concentration and just put down he first thing I saw.
So to find the moles of V ion would I multiply 0.0036 by the ratio?

Answer 12

So you want to rearrange the formula for molarity (mol/L) to solve for the unknown (moles in this case) then plug in the right values.

Were trying to find moles so that is the unknown. We know the molarity is 0.0036 mol/L from the question itself, but the volume is not in the correct units, so we have to convert it.

mL to L is 1000-fold, 1000 mL = 1 L; 10.5 mL is 0.0105 L

\(\sf Molarity =\dfrac{moles}{L}\rightarrow moles=L*Molarity =\)

\(\sf moles =0.0105 L*0.0036~mol/L\)

This number is the number of moles of the molecule \(VO_2^+\), since it has 1 V in the formula, it's also the moles of V.

Now if we multiply by 3 it, we get the moles of Zn needed.

Finally, we need to convert moles to grams.

\(\sf moles=\dfrac{mass}{Molar ~mass}\)

What is the Molar mass of Zn?

Answer 13

The molar mass of Zn is 65.41. So if I do 0.0001134 mol Zn/65.41 = 1.73 x 10^-6 g Zn.
Correct?

Answer 14

I tried to answer 1.73 x10^-6 and 1.7 x 10^-6 and both were wrong. Is there something else I need to do?

Answer 15

you didn't follow the formula correctly.

\(\sf moles=\dfrac{mass}{Molar~mass}\)

Out of these variables you knew the moles and the Molar mass, the unknown was mass, thus,

\(\sf mass=moles*Molar~mass= 0.0001134 ~mol ~Zn*65.41~g/mol \)