Chapter 18: Q. 55 (page 513)

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

Short Answer

Expert verified

The volume of the liquid water is $V = 92.73 c m 3$

Step by step solution

Given information

The volume of steam $V_{s} = 10000 {cm}^{3}$

The temperature of the steam $T_{s} = 200 + 273 = 473 K$

Pressure $P = 20 atm$

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

$P V = n R T$

calculation

Description

Steps

Step:1 the number moles calculating

$n = \frac{P V_{s}}{R T_{s}} = \frac{(20 atm) (10000 {cm}^{3})}{82.057 {cm}^{3} {atmKmol}^{- 1}} n = 5.152 mol$

Step:2 calculating the volume of water

$m a s s = n u m b e r o f m o l e s \times M o l a r m a s s$

= 5.152 \times 18 = 92.736 g VolumeV = m / ρ = \frac{92.736 g}{{Ig}^{g} {cm}^{3}} V = 92.736 {cm}^{3}

$= 5.152 \times 18 = 92.736 g VolumeV = m / ρ = \frac{92.736 g}{{Ig}^{2} / {cm}^{3}} V = 92.736 {cm}^{3}$

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

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

Short Answer

Step by step solution

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10,000cm3of 200°Csteam at a pressure of 20atmis cooled until it condenses. What is the volume of liquid water? Give your answer in cm3.

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Step by step solution

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calculation

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