Question

Calculate the final temperature, in degrees Celsius, ∘C, for each of the following with n and V constant.
Part A
A sample of helium gas with a pressure of 250 torr at 0∘C is heated to give a pressure of 2500 torr .
Express your answer to two significant figures and include the appropriate units.
T = ???
Part B
A sample of air at 21 ∘C and 800 mmHg is cooled to give a pressure of 610 mmHg .
Express your answer to two significant figures and include the appropriate units.
T = ???

Answer 1

Answer on Question #56047 - Chemistry - General chemistry

Question:

Calculate the final temperature, in degrees Celsius, $^\circ \mathrm{C}$, for each of the following with n and V constant.

Part A

A sample of helium gas with a pressure of 250 torr at $0^\circ \mathrm{C}$ is heated to give a pressure of 2500 torr.

Express your answer to two significant figures and include the appropriate units.

T = ???

Part B

A sample of air at $21^\circ \mathrm{C}$ and $800\ \mathrm{mmHg}$ is cooled to give a pressure of $610\ \mathrm{mmHg}$.

Express your answer to two significant figures and include the appropriate units.

T = ???

Solution:

Part A

For the isochoric process, the following ratio is valid:

$$\frac{p_1}{T_1} = \frac{p_2}{T_2}$$

Then, if the initial conditions are 273.15 K (0 °C) and 250 torr, the final conditions will be T2 and 2500 torr.

$$T_2 = \frac{p_2 T_1}{p_1} = \frac{2500 \cdot 273.15}{250} = 2.7 \cdot 10^3 K, \text{ or } 2.5 \cdot 10^{3^\circ} \mathrm{C}$$

Part B

With the same ratio used for the part A $p_2$ is 610 mm Hg, $T_1$ is 294.15 K, $p_1$ is 800 mm Hg:

$$T_2 = \frac{p_2 T_1}{p_1} = \frac{610 \cdot 294.15}{800} = 2.2 \cdot 10^2 K, \text{ or } -49^\circ \mathrm{C}$$

Answer: Part A $2.5 \cdot 10^{3^\circ} \mathrm{C}$, Part B $-49^\circ \mathrm{C}$

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