Chapter 2, Problem 104A

Interpretation Introduction

Interpretation:

The density and mass of zinc sample needs to be represented in correct number of significant figures.

Concept introduction:

Density of a sample of matter or an object is equal to the mass of the sample divided by the volume of the sample.

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

Answer to Problem 104A

Density of the zinc sample is $\text{7}\text{.15}\text{g/mL}$. Density and mass of the zinc sample should be in three significant figures.

Explanation of Solution

Given Information:

For the first zinc sample, the mass is $\text{210}\text{.10}\text{g}$ and for second sample, the mass is $\text{235}\text{.10}\text{g}$. The combined volume of two samples is $\text{62}\text{.3}\text{mL}$.

The answer (mass of the zinc) must go to hundredths place as both the masses go to this decimal place.

Total mass of the zinc sample = 210.10 g + 235.10 g

= 445.30 g

Now, the density can be calculated by dividing mass of the zinc sample by its volume. When dividing, number of the significant figures should not exceed the least amount of the significant figures in both the values. The value of volume contains three significant figures while the value of the mass contains five significant figures. So, the final answer i.e. density should be in three significant figures.

$\begin{array}{c}\text{Density}=\frac{\text{Mass}}{\text{Volume}}\\ =\frac{445.10\text{g}}{\text{62}\text{.3}\text{mL}}\\ =\text{7}\text{.15}\text{g/mL}\end{array}$

Conclusion

Density of the zinc sample is $\text{7}\text{.15}\text{g/mL}$. Density and mass of the zinc sample should be in three significant figures.