Chapter 2, Problem 1SAQ

Two samples of a compound containing elements A and B are decomposed. The first sample produced15 g of A and 35 g of B. The second sample produced25 g of A and what mass of B?

a) 11 g

b) 58 g

c) 21 g

d) 45 g

Interpretation Introduction

Interpretation: The mass of element B present in the second sample is to be determined.

Concept Introduction: Joseph Proust in 1797, gave a law of definite proportion. According to this law, all the samples of a compound contains same proportion of their constituent elements regardless of whatever the source of the compound.

Answer to Problem 1SAQ

Correct answer: The mass of B produced by sample 2 is $58\text{ g}$. Therefore, option (b) is correct.

Explanation of Solution

Justify reasons for the correct statement:

In accordance with the law of definite proportions, the mass of constituent elements in all the samples of a given compound are in the same proportion. This means, in first sample the total mass of a compound i.e.$50\text{ g}$ produces $15\text{ g}$ of A and $35\text{ g}$ of B. Calculate the ratio of A over B as follows:

$\begin{array}{c}\text{Ratio}=\frac{\text{Mass of A}}{\text{Mass of B}}\\ =\frac{15\text{ g}}{35\text{ g}}\\ =\frac{3}{7}\end{array}$

Thus, $\text{A}:\text{B}$ is $3:7$.

As the ratio of the constituent elements in a compound remains same. Therefore, this ratio is used to calculate the mass of B. Calculate the mass of B as follows:

$\begin{array}{c}\frac{\text{Mass of A }\left(\text{sample 1}\right)}{\text{Mass of B }\left(\text{sample 1}\right)}=\frac{\text{Mass of A }\left(\text{sample 2}\right)}{\text{Mass of B }\left(\text{sample 2}\right)}\\ \frac{15\text{ g}}{35\text{ g}}=\frac{25\text{ g}}{\text{Mass of B }\left(\text{sample 1}\right)}\end{array}$

Rearrange the above expression as follows:

$\begin{array}{c}\text{Mass of B }\left(\text{sample 1}\right)=\frac{25\text{ g}\times 35\text{ g}}{15\text{ g}}\\ =58\text{ g}\end{array}$

Justify reasons for the correct statement:

Option (a) is incorrect because according to the above calculations, the mass of element B cannot be obtained as $11g$.

Option (c) is incorrect because according to the above calculations, the mass of element B cannot be obtained as $21g$.

Option (d) is incorrect because according to the above calculations, the mass of element B cannot be obtained as $45g$.

Conclusion

The correct answer is option (b).