Chapter 10, Problem 172A

Interpretation Introduction

Interpretation:

Empirical formula of monosodium glutamate needs to be found for which % of C, H, O, N and Na are is 35.5, 4.77, 39.9, 8.29 and 13.6 respectively.

Concept introduction:

Empirical formula of a molecule is the smallest unit which is repeated in the molecule.

Answer to Problem 172A

The empirical formula is C₅H₈O₄NNa.

Explanation of Solution

% of C, H, O, N and Na are 35.5, 4.77, 39.9, 8.29 and 13.6 respectively. Assuming 100 g of the compound, mass of C, H, O, N and Na is 35.5 g, 4.77 g, 39.9 g, 8.29 g and 13.6 g respectively.

The molar mass of C, H, O, N and Na is 12 g/mol, 1 g/mol, 16 g/mol, 14 g/mol and 23 g/mol respectively.

The number of moles of each element can be calculated as follows:

Moles of C $\text{=}\frac{\text{35}\text{.5}}{\text{12}}\text{=2}\text{.958}\text{.}$

Moles of H $=\frac{4.77}{1}=\mathrm{4.77.}$

Moles of O $=\frac{39.9}{16}=\mathrm{2.494.}$

Moles of N $=\frac{8.29}{14}=\mathrm{0.592.}$

Moles of Na $=\frac{13.6}{23}=\mathrm{0.591.}$

Now,

Smallest mole ratio C: H: O: N: Na $\begin{array}{l}=\frac{2.958}{0.591}:\frac{4.77}{0.591}:\frac{2.494}{0.591}:\frac{0.592}{0.591}:\frac{0.591}{0.591}\\ =5.005:8.07:4.22:1.002:1\approx 5:8:4:1:1.\end{array}$

Thus, empirical formula is C₅H₈O₄NNa.

Conclusion

Empirical formula of monosodium glutamate is C₅H₈O₄NNa.