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# Volume Change to 100mL

ACTSCI-1KO6BH

A student studying the relationship between the pressure, temperature, and volume of a gas derives the following relationship:

$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$

The student then conducts a series of experiments to test the relationship:

Experiment 1

The student first decides to test the relationship between pressure and volume by keeping the temperature constant at 25°C. She uses a rigid container with a movable plunger as shown below.

The student starts with the plunger at 500. mL and a pressure of 500. mmHg of helium gas in the container. The student then moves the plunger to different volumes and measures the pressure. The table below summarizes the results.

Table 1

Trial Volume (mL) Pressure (mmHg)
1 500 500
2 750 376
3 1000 251
4 250 748

Experiment 2

In a second experiment, the student takes the plunger and places it in a temperature controlled water bath. Once again, the student locks the plunger at 500 mL and fills the container with helium gas. The student then varies the temperature and records the pressure of the gas in the container. Table 2 below summarizes the results.

Table 2

Trial Temperature $^\circ$C Pressure (mmHg)
5 20 500
6 40 534
7 60 568
8 80 602

Experiment 3

In a final experiment, the student decides to places 4 different gases in the container at initial pressures of 500. mmHg and initial volumes of 500. mL. The student then depresses the plunger to a volume of 250. mL and measures the new pressure. Table 3 below summarizes the results.

Table 3

Trial Gas Volume (mL) Pressure (mmHg)
9 Helium 4.003 1000
10 Neon 20.18 1001
11 Argon 39.95 999
12 Xenon 83.80 999

If the volume of the gas in experiment 1 were reduced to 100 mL which of the following would be the closest to the pressure of the gas?

A

$2510$

B

$747$

C

$500$

D

$74.8$