Question

A) The substance sulfur dioxide has the following properties:

normal melting point:	200.4 K
normal boiling point:	263.1 K
triple point:	1.7×10-3 atm, 197.6 K
critical point:	78 atm, 430.7 K

A sample of sulfur dioxide at a pressure of 1.00 atm and a temperature of 253.5 K is cooled at constant pressure to a temperature of 192.3 K. Which of the following are true?

Choose all that apply

The solid initially present will vaporize.

The sample is initially a liquid.

The final state of the substance is a solid.

One or more phase changes will occur.

The final state of the substance is a liquid.

B) The substance xenon has the following properties:

normal melting point:	161.3 K
normal boiling point:	165.0 K
triple point:	0.37 atm, 152.0 K
critical point:	57.6 atm, 289.7 K

A sample of xenon is initially at a pressure of 63.9 atm and a temperature of 178.0 K. The pressure on the sample is reduced to 0.370 atm at a constant temperature of 178.0 K. Which of the following are true?

Choose all that apply

The sample is initially a liquid.

The liquid initially present will solidify.

One or more phase changes will occur.

The final state of the substance is a solid.

The final state of the substance is a gas.

Answer 1

A)

Note that a sample that lies below normal melting point at 1.00 atm must be a solid while a sample that lies in between melting point and boiling point is a gas and a sample that lies above boiling point is a gas.

The sample is initially at 1.00 atm and 253.5 K. Since the normal melting point of SO₂ is given to be 200.4 K (solid-liquid boundary ) and normal boiling point is 263.1 K(liquid-gas boundary), it must exist as a liquid at 253.5 K.

Further, the temperature is being dropped to 192.3 K, which is lower than the melting point of 200.4 K. Hence, the final state of the compound is a solid.

Hence, the liquid is condensing to form a solid as the temperature changes from 253.5 K to 192.3 K at 1.00 atm.

Lets analyse each of the given options based on the given data for SO₂.

• The solid initially present will vaporize.

Verdict: False

Reason: Since the sample is initially a liquid and changes to solid, the statement is false.

• The sample is initially a liquid.

Verdict: True

Reason: The initial temperature of the sample lies between melting point and boiling point at 1.00 atm. Hence, it is a liquid.

• The final state of the substance is a solid.

Verdict: True

Reason: The temperature is being dropped to 192.3 K which is lower than the melting point of 200.4 K. Hence, the liquid is changing to a solid.

• One or more phase changes will occur.

Verdict: True

Reason: Since the liquid is condensing to form solid, one phase change is occurring.

• The final state of the substance is liquid.

Verdict: False

Reason: The final state of the substance is a solid as explained above.

Hence, you have to choose second, third and fourth statement as true statements.

B)

The sample is initially at 63.9 atm and a temperature of 178.0 K.

Note that the pressure is much higher than normal pressure of 1.00 atm. It is given that the critical point of xenon is 57.6 atm and 289.7 K. Since our temperature of 178.0 K is lower than the critical temperature, the sample initially must be a liquid.

Also note that the boiling point is 165.0 K at 1.00 atm, but we will not be able to convert the sample to gas simply by changing the temperature because of the high pressure it is in which keeps it as a liquid. Hence, pressure must be lowered for it to boil.

(Visualization of phase diagram helps here, where the point will lie far above in liquid region)

Finally ,the sample is lowered in pressure to 0.37 atm at constant temperature of 178.0 K.

Since the pressure is lower than normal pressure of 1.00 atm and temperature is higher than boiling point of 165.0 K, the final state of the sample will be gas.

Now, we can analyse each of the given options with the data above:

• The sample is initially a liquid.

Verdict: True

Reason: Because it lies in high pressure and moderate temperature above boiling point, it must be a liquid.

• The liquid initially present will solidify.

Verdict: False

Reason: Since the pressure is being decreased ,the liquid will change to a gas.

• One or more phase changes will occur.

Verdict: True

Reason: The pressure is being dropped enough and temperature is high enough to cause phase change to a less dense gaseous phase. Hence, one phase change is happening.

• The final state of the substance is solid.

Verdict: False

Reason: The final state of the substance is a gas. Hence, it is false.

• The final state of the substance is a gas.

Verdict: True

Reason: As explained above.

Hence, the first , third and fifth statement are true.