Answer:
0.64 M
Explanation:
Given:
Volume of iron(II) solution (V₁) = 25.0 mL = 0.025 L
Molarity of iron(II) solution (M₁) = ?
Number of moles of iron(II) solution (n₁) = ?
Volume of dichromate solution (V₂) = 18.0 mL = 0.018 L
Molarity of dichromate solution (M₂) = 0.145 M
Number of moles of dichromate solution (n₂) = ?
Molarity is equal to the ratio of moles and volume.
So, molarity of dichromate solution is given as:
![M_2=\frac{n_2}{V_2}\\\\n_2=M_2\times V_2=0.145\times 0.018 = 2.61\times 10^{-3}\ mol](https://tex.z-dn.net/?f=M_2%3D%5Cfrac%7Bn_2%7D%7BV_2%7D%5C%5C%5C%5Cn_2%3DM_2%5Ctimes%20V_2%3D0.145%5Ctimes%200.018%20%3D%202.61%5Ctimes%2010%5E%7B-3%7D%5C%20mol)
Now, let us write the complete balanced reaction for the given situation.
So, the complete balanced equation is given below.
![6Fe^{2+}(aq)+Cr_2O_7^{2-}(aq)+14H^+(aq)\to 6Fe^{3+}(aq)+2Cr^{3+}(aq)+7H_2O](https://tex.z-dn.net/?f=6Fe%5E%7B2%2B%7D%28aq%29%2BCr_2O_7%5E%7B2-%7D%28aq%29%2B14H%5E%2B%28aq%29%5Cto%206Fe%5E%7B3%2B%7D%28aq%29%2B2Cr%5E%7B3%2B%7D%28aq%29%2B7H_2O)
From the equation, it is clear that, 1 mole of dichromate is required for 6 moles of iron(II) solution.
So, using unitary method, we find the number of moles of iron(II) solution.
1 mole of dichromate = 6 moles of iron(II)
∴ n₂ moles of dichromate = 6n₂ moles of iron(II)
= ![6\times 2.61\times 10^{-3}=0.016\ mol\ Fe^{2+}](https://tex.z-dn.net/?f=6%5Ctimes%202.61%5Ctimes%2010%5E%7B-3%7D%3D0.016%5C%20mol%5C%20Fe%5E%7B2%2B%7D)
So, 0.016 moles of iron(II) is needed. Therefore, ![n_1=0.016\ mol](https://tex.z-dn.net/?f=n_1%3D0.016%5C%20mol)
Now, molarity of iron(II) solution is given as:
Molarity = Moles ÷ Volume
![M_1=\frac{n_1}{V_1}\\\\M_1=\frac{0.016\ mol}{0.025\ L}=0.64\ M](https://tex.z-dn.net/?f=M_1%3D%5Cfrac%7Bn_1%7D%7BV_1%7D%5C%5C%5C%5CM_1%3D%5Cfrac%7B0.016%5C%20mol%7D%7B0.025%5C%20L%7D%3D0.64%5C%20M)
Therefore, the molarity of the iron(II) solution is 0.64 M.