Question

$10,000{\mathrm{cm}}^3$of $200°\mathrm{C}$steam at a pressure of $20\mathrm{atm}$is cooled until it condenses. What is the volume of liquid water? Give your answer in ${\mathrm{cm}}^3$.

Short answer

The volume of the liquid water is$V=92.73cm3$

Step-by-step solution

Given information 

The volume of steam$V_s=10000{\mathrm{cm}}^3$

The temperature of the steam$T_s=200+273=473K$

Pressure$P=20\mathrm{atm}$

The number of molecules remains constant. Using the given data, the number of moles can be found and by substituting density, the volume of water can be found.

formula used:

Ideal gas law

$PV=nRT$

calculation

Description	Steps
Step:1 the number moles calculating	$$\begin{gathered} n=\frac{P{V}_s}{R{T}_s} \\ =\frac{(20\mathrm{atm})\left(10000{\mathrm{cm}}^3\right)}{82.057{\mathrm{cm}}^3{\mathrm{atmKmol}}^{-1}} \\ n=5.152\mathrm{mol} \end{gathered}$$
Step:2 calculating the volume of water	$mass=numberofmoles\times Molarmass$ $$\begin{gathered} =5.152\times 18 \\ =92.736\mathrm{g} \\ \text{VolumeV}=\mathrm{m}/\rho \\ =\frac{92.736\mathrm{g}}{{\mathrm{Ig}}^{\mathrm{g}}{\mathrm{cm}}^3} \\ V=92.736{\mathrm{cm}}^3 \end{gathered}$$ $$\begin{gathered} =5.152\times 18 \\ =92.736g \\ \text{VolumeV}=m/\rho \\ =\frac{92.736g}{{\mathrm{Ig}}^2/{\mathrm{cm}}^3} \\ V=92.736{\mathrm{cm}}^3 \end{gathered}$$

Hence $V=92.736{\mathrm{cm}}^3$represents the volume of water.