Chapter 1.2, Problem 11R

To determine

The density of an unknown metal.

Answer to Problem 11R

The density of the metal is $\boxed{d=7900{\text{ kg/m}}^{\text{3}}}$ and the metal is iron.

Explanation of Solution

Given:

Mass of the metal is $m=158\text{ gm}$ .

Volume is $v=20\text{ mL}$ .

Formula used:

The expression for density is,

  $d=\frac{\text{mass}}{\text{volume}}=\frac{m}{v}$....................(1)

Here, d is the density, m is the mass and v is the volume.

Calculation:

Substitute 158 gm for m and 20 mL for vequation (1)

  $\begin{array}{l}d=\frac{158\text{ gm}}{20\text{ mL}}\\ d=7.9\text{ gm/mL}\\ d=7.9\frac{\left(\text{gm×}\frac{\text{1}\text{kg}}{\text{1000}\text{gm}}\right)}{{10}^{-3}\text{L}}\\ d=7.9(0.001\text{ kg}/{10}^{-6}{\text{m}}^{\text{3}})\\ \boxed{d=7900{\text{ kg/m}}^{\text{3}}}\end{array}$

Conclusion:

Hence, the density of the metal is $\boxed{d=7900{\text{ kg/m}}^{\text{3}}}$ and the metal is iron.