Question

A liquid solvent is added to a flask containing an insoluble solid. The total volume of the solid and liquid together is 84.0 mL. The liquid solvent has a mass of 26.5 g and a density of 0.865 g/mL. Determine the mass of the solid given its density is 3.25 g/mL.

Answer 1

Answer:

The mass of solid is 173.45 g.

Explanation:

Given that,

Total volume of solid and liquid = 84.0 mL

Mass of liquid = 26.5 g

Density of liquid = 0.865 g/mL

Density of solid = 3.25 g/mL

We need to calculate the volume of liquid

Using formula of density

$\rho_{l}=\dfrac{m_{l}}{V_{l}}$

$V_{l}=\dfrac{m_{l}}{\rho_{l}}$

Put the value into the formula

$V_{l}=\dfrac{26.5}{0.865}$

$V_{l}=30.63\ mL$

We need to calculate the volume of solid

Volume of solid = Total volume of solid and liquid- volume of liquid

$V_{s}=84.0-30.63$

$V_{s}=53.37\ mL$

We need to calculate the mass of solid

Using formula of density

$\rho_{s}=\dfrac{m_{s}}{V_{s}}$

$m_{s}=\rho_{s}\timesV_{s}$

Put the value into the formula

$m_{s}=3.25\times53.37$

$m_{s}=173.45\ g$

Hence, The mass of solid is 173.45 g.

Answer 2

Answer:

$m_s=173.4335\ g$

Explanation:

Given:

• total volume of insoluble solid and a liquid solvent, $V=84\ mL$

• mass of liquid, $m_l=26.5\ g$

• density of liquid, $\rho_l=0.865\ g.mL^{-1}$

• density of solid, $\rho_s=3.25\ g.mL^{-1}$

Now the volume of liquid:

$V_l=\frac{m_l}{\rho_l}$

as density is mass per unit volume.

$V_l=\frac{26.5}{0.865}$

$V_l=30.6358\ mL$

Therefore the volume of the solid:

$V_s=V-V_l$

$V_s=84-30.6358$

$V_s=53.3642\ mL$

Now the mass of the solid:

$m_s=\rho_s\times V_s$

$m_s=3.25\times 53.3642$

$m_s=173.4335\ g$