Answer:
The concentration of the Potassium Dichromate solution is 0.611 M
Explanation:
First of all, we need to understand that in the final solution we'll have potassium ions coming from KBr and also K2Cr2O7, so we state the dissociation equations of both compounds:
KBr (aq) → K+ (aq) + Br- (aq)
K2Cr2O7 (aq) → 2K+ (aq) + Cr2O7 2- (aq)
According to these balanced equations when 1 mole of KBr dissociates, it generates 1 mole of potassium ions. Following the same thought, when 1 mole of K2Cr2O7 dissociates, we obtain 2 moles of potassium ions instead.
Having said that, we calculate the moles of potassium ions coming from the KBr solution:
0.19 M KBr: this means that we have 0.19 moles of KBr in 1000 mL solution. So:
1000 mL solution ----- 0.19 moles of KBr
253 mL solution ----- x = 0.04807 moles of KBr
As we said before, 1 mole of KBr will contribute with 1 mole of K+, so at the moment we have 0.04807 moles of K+.
Now, we are told that the final concentration of K+ is 0.846 M. This means we have 0.846 moles of K+ in 1000 mL solution. Considering that volumes are additive, we calculate the amount of K+ moles we have in the final volume solution (441 mL + 253 mL = 694 mL):
1000 mL solution ----- 0.846 moles K+
694 mL solution ----- x = 0.587124 moles K+
This is the final quantity of potassium ion moles we have present once we mixed the KBr and K2Cr2O7 solutions. Because we already know the amount of K+ moles that were added with the KBr solution (0.04807 moles), we can calculate the contribution corresponding to K2Cr2O7:
0.587124 final K+ moles - 0.04807 K+ moles from KBr = 0.539054 K+ moles from K2Cr2O7
If we go back and take a look a the chemical reactions, we can see that 1 mole of K2Cr2O7 dissociates into 2 moles of K+ ions, so:
2 K+ moles ----- 1 K2Cr2O7 mole
0.539054 K+ moles ---- x = 0.269527 K2Cr2O7 moles
Now this quantity of potassium dichromate moles came from the respective solution, that is 441 mL, so we calculate the amount of them that would be present in 1000 mL to determine de molar concentration:
441 mL ----- 0.269527 K2Cr2O7 moles
1000 mL ----- x = 0.6112 K2Cr2O7 moles = 0.6112 M
= 6.02x10⁻⁶