Chapter U3.3, Problem 5E

Interpretation Introduction

Interpretation : Volume of liquid water that results after melting 24mLof ice is to be calculated.

Concept Introduction : If the volume of ice is given, one can convert volume of ice to volume of water by using mathematical equations.

When ice melts, its volume decreases but its mass remains the same as liquid water is formed.

Answer to Problem 5E

The formula to calculate mass of a substance is given by:

  $\begin{array}{l}\text{Mass(m)=Density(D)×Volume(V)}\\ \text{m=D×V}\end{array}$

Volumeof water formed from melting of 24mLof ice is 22.08mL

Explanation of Solution

When ice melts, its volume decreases but the mass of water formed after melting remains the same. This is because the same water molecules are present in solidice and melted ice. Density of ice is less than density of water. One can use density equation to convert between mass and volume.

The formula to calculate mass of a substance is given by:

  $\begin{array}{l}\text{Mass(m)=Density(D)×Volume(V)}\\ \text{m=D×V}\end{array}$

Mass of ice can be calculated as follows:

Given: $\text{volume of ice=24mL}$

  $\begin{array}{l}\text{Density of ice=0}\text{.92g/mL}\\ \text{m(ice)=D(ice)}\times \text{V(ice)}\\ \text{m(ice)=0}\text{.92}\times \text{24=22}\text{.08g}\end{array}$

Mass of rain water is equal to mass of ice

  $\text{m(ice)=m(water)=22}\text{.08g}$

One can calculate volume of water as follows:

  $\begin{array}{l}\text{V(water)=}\frac{\text{m(water)}}{\text{D(water)}}\\ \text{=}\frac{\text{22}\text{.08}}{\text{1}}\text{=22}\text{.08mL}\end{array}$

(Density of water is taken as 1.0g/mL

Conclusion

Mathematical equations can be used to calculate volume or mass of ice and water. To use mathematical equations, we must know the density of ice and density of liquid water.