A group of students conducted an experiment to study the relationship between the pressure… — ACT

A group of students conducted an experiment to study the relationship between the pressure and volume of a gas sample at a constant temperature. The gas was contained in a cylinder equipped with a movable piston. By adjusting the piston, the students varied the volume of the gas ( $V$ , in liters) and measured the resulting pressure ( $P$ , in atmospheres). The results are recorded in the table below.

Trial	Volume ( $V$ , $\text{L}$ )	Pressure ( $P$ , $\text{atm}$ )
1	$1.5$	$8.0$
2	$3.0$	$4.0$
3	$6.0$	$2.0$
4	$12.0$	$1.0$

If the students perform a fifth trial and adjust the piston to a volume of $4.0\text{ L}$ , which of the following is the most likely pressure of the gas sample?

A
$1.3\text{ atm}$
$3.0\text{ atm}$ Answer
C
$5.3\text{ atm}$
D
$48.0\text{ atm}$

Answer

3.0\text{ atm}

The correct answer is the option stating

3.0\text{ atm}

. The data in the table shows that pressure (

P

) and volume (

V

) are inversely proportional because their product is constant across all trials:

P \times V = 1.5 \times 8.0 = 3.0 \times 4.0 = 6.0 \times 2.0 = 12.0\text{ L}\cdot\text{atm}

. For a volume of

4.0\text{ L}

, the pressure is calculated as

P = \frac{12.0}{4.0} = 3.0\text{ atm}

Step-by-Step Solution

Analyze the relationship between volume (

V

) and pressure (

P

) in the table.

As the volume increases from

1.5

12.0\text{ L}

, the pressure decreases from

8.0

1.0\text{ atm}

. The product of pressure and volume remains constant for all trials:

P \times V = 12.0\text{ L}\cdot\text{atm}

. This indicates that pressure and volume are inversely proportional.

To identify whether the variables have a direct or inverse relationship and determine the constant of proportionality.

Apply the inverse proportionality equation to find the pressure for the new volume of

4.0\text{ L}

P = \frac{12.0\text{ L}\cdot\text{atm}}{4.0\text{ L}} = 3.0\text{ atm}

To calculate the expected pressure when the volume is set to

4.0\text{ L}

using the determined relationship.

Key Concept

Inverse proportionality dictates that as one variable increases, the other decreases such that their product remains constant (

y \propto \frac{1}{x}

, or

x \times y = k

Estimated Time:1m 30s

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Step-by-Step Solution

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