Question

A liquid solvent is added to a flask containing an insoluble solid. The total volume of the solid and liquid together is 91.0 mL.

The liquid solvent has a mass of 28.6 g
and a density of 0.865 g/mL.
Determine the mass of the solid given its density is 3.00 g/mL.

Answer 1

Determine the mass of the solid : 173.809 g

Explanation:

We are given the total volume = 91 ml

Mass of liquid solvent = 28.6 g
Density of liquid solvent = 0.865 g/ml

Volume of an object = mass / density

Volume of liquid solvent = 28.6 g / 0.865 g/ml
= 33.06358 ml

Volume of solid solvent = Total volume - Volume of liquid solvent
= 91.0 - 33.06358
= 57.93642 ml

Density of solid solvent = 3 g/ml

We have the relationship: Volume = mass x density or
Mass = Volume x density

Mass of solid solvent = Volume of solid solvent x Density of solid solvent
= 57.93642 ml x 3 g/ml

= 173.80926 g

≈ 173.809 g

Answer 2

Explanation:

Let's use the principle of mass balance to solve this problem. We know that the total mass of the system (solid + liquid) is conserved. Therefore:

mass of solid + mass of liquid = total mass

Let's represent the mass of the solid by m. We can find the mass of the liquid by using its volume and density:

mass of liquid = volume of liquid x density of liquid

mass of liquid = 28.6 g

density of liquid = 0.865 g/mL

volume of liquid = mass of liquid / density of liquid

volume of liquid = 28.6 g / 0.865 g/mL

volume of liquid = 33.08 mL

Now we can use the total volume to find the volume of the solid:

total volume = volume of solid + volume of liquid

volume of solid = total volume - volume of liquid

volume of solid = 91.0 mL - 33.08 mL

volume of solid = 57.92 mL

We are given the density of the solid (3.00 g/mL), so we can find its mass using its volume:

mass of solid = volume of solid x density of solid

mass of solid = 57.92 mL x 3.00 g/mL

mass of solid = 173.76 g

Therefore, the mass of the solid is 173.76 g.