Suppose that you have confined some water vapor, a gas, to 50.00000 ml at 25.00d

Question

Suppose that you have confined some water vapor, a gas, to 50.00000 ml at 25.00degreeC and mm g. Calculate the number of moles of gas in this sample.  Calculate the number of molecules of gas in this sample.  Calculate the filled volume that is occupied by just the atoms of the water molecules themselves. This excludes the void space that is between the atoms of the water molecules.  Remember that the total volume that is taken up by the molecules is nominally 50.00000 ml, which includes the void space, since a gas expands to fill its container. Most of the 50.00000 ml is void space. Calculate percentage of void space in this gas.  Changes of state involve the separation of molecules from each other. Based on your calculations of percent void space, which phase change should have the largest enthalpy change, melting or boiling? Explain

Explanation / Answer

21)

V = 50 ml = 50/1000 L

T = 25 °C = 298 K

P = 742.2 mm Hg = 742.2/760 atm

n = PV/(RT) = 742.2/760 * (50/1000) / (0.082*298) = 0.001998238

22)

number of molecules

1 mol = 6.022*10^23 molecules

0.001998238 mol = 0.001998238*6.022*10^23 = 1.203*10^21 molecules

23)

the volume occupied just by water

for water = 2.99 × 10²³ cm3 per molecule

since we have

1.203*10^21

then 1.203*10^21*(2.99*10^-23) = 0.0359697 cm3 or ml

24)

void space = 50 - 0.0359697 = 49.9640303

then

% void = (50-0.0359697 )/(50) *100 = 99.9280%

25)

larges enthalpy change should be boiling, since gas are very separated molecules

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