Question

Retinol is vitamin A and one of the components in multivitamin tablets. A 213.0 mg sample of retinol was dissolved in 1.000 g of chloroform (Kb = 3.630°C/m), increasing the boiling point of chloroform by 2.699°C.

1.Calculate the molar mass of retinol.

2.Retinol is 83.84% C, 10.58% H, and 5.58% O by mass. What is the molecular formula of retinol? Add the missing subscripts.

Answer 1

Answer on question 80853 – Chemisrty – General Chemistry

1) In the base, let's get formula "The Change in Freezing Point Equation":

$$\Delta \mathrm {T} = \mathrm {i} ^ {*} \mathrm {m} ^ {*} \mathrm {K}, \text { where i - van't Hoff factor, m - molality(moles solute/kg solvent), K - boiling point elevation;}$$

In our way, $\mathrm{K} = 3.63^{\circ}\mathrm{C / m}$, $\Delta \mathrm{T} = 2.699^{\circ}\mathrm{C}$, $\mathrm{i} = 1$ (nonelectrolytes), we ought to find molality:

$$\mathrm {m} = \Delta \mathrm {T} / \mathrm {i} ^ {*} \mathrm {K} = 2.699 / 1 * 3.63 = 0.744 \text{ moles/kg};$$

So, $\mathrm{m} = \mathrm{X / kg}$; $\mathrm{X} = \mathrm{m}^{*}\mathrm{kg} = 0.744^{*}0.001 = 0.000744$ moles;

$\mathrm{M(molar~mass)} = \mathrm{m(retinol) / X} = 0.213 / 0.000744 = 286.3~\mathrm{g / m / moles};$

2) $\mathrm{w(C)} = 83.84\%$, $\mathrm{w(H)} = 10.58\%$, $\mathrm{w(O)} = 5.58\%$; Formula - ?:

$$\mathrm {C} _ {\mathrm {x}} \mathrm {H} _ {\mathrm {y}} \mathrm {O} _ {\mathrm {z}}$$

Let's find quantity of atoms:

$$\begin{array}{l} \mathrm {n (C)} = 286.3 * 83.84 / 12 * 100 = 20; \\ \mathrm {n (H)} = 286.3 * 10.58 / 1 * 100 = 30.3; \\ \mathrm {n (O)} = 286.3 * 5.58 / 16 * 100 = 1; \\ \end{array}$$

We can say, that $\mathrm{x} = 20$; $\mathrm{y} = 30$; $\mathrm{z} = 1$ and formula has view $\mathrm{C}_{20}\mathrm{H}_{30}\mathrm{O}$.

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