Chapter 13, Problem 1CQ

Which has the greater density, 1 g of mercury or 1000 g of water?

To determine

To find: The substance which has greater density.

Answer to Problem 1CQ

The substance which has greater density is 1 g of mercury.

Explanation of Solution

Given data:

The mass of mercury is 1 g and the mass of water is 1000 g.

Explanation:

Refer to Table 13.1 in the textbook for the densities of fluids at 1 atm pressure.

The density is basically estimated as ratio to the mass to volume, even though the density does not depend on object size. Therefore, the density remains same irrespective of mass either it is 1 g or 1000 g. The density is unchanged for any shape or volume and mass of a specific substance.

From Table 13.1, the density of mercury $\left({\rho }_{\text{mercury}}\right)$ is $13,600\frac{\text{kg}}{{\text{m}}^{\text{3}}}$ and the density of water $\left({\rho }_{\text{water}}\right)$ is $1000\frac{\text{kg}}{{\text{m}}^{\text{3}}}$.

Find the value of ratio $\frac{{\rho }_{\text{mercury}}}{{\rho }_{\text{water}}}$.

$\begin{array}{c}\frac{{\rho }_{\text{mercury}}}{{\rho }_{\text{water}}}=\frac{13,600\frac{\text{kg}}{{\text{m}}^{\text{3}}}}{1000\frac{\text{kg}}{{\text{m}}^{\text{3}}}}\\ =13.6\end{array}$

Re-arrange the expression.

${\rho }_{\text{mercury}}=13.6{\rho }_{\text{water}}$

Therefore, the density of 1 g of mercury is $13.6$ times higher than the density of 100 g of water.

Conclusion:

Thus, the substance, which has greater density is 1 g of mercury.