Question

a 3.50 l sample of hydrogen gas has a pressure of 0.750 atm. what is its volume if its pressure is increased to 1.50 atm at constant temperature? 2.90 l 4.35 l 1.75 l 3.95 l

Explanation:

Step1: Identify the gas law

This is a problem of Boyle's Law, which states that for a given amount of gas at constant temperature, the product of pressure and volume is constant, i.e., \( P_1V_1 = P_2V_2 \).

Step2: List the given values

We have \( P_1 = 0.750 \, \text{atm} \), \( V_1 = 3.50 \, \text{L} \), and \( P_2 = 1.50 \, \text{atm} \). We need to find \( V_2 \).

Step3: Rearrange the formula to solve for \( V_2 \)

From \( P_1V_1 = P_2V_2 \), we can solve for \( V_2 \) as \( V_2=\frac{P_1V_1}{P_2} \).

Step4: Substitute the values into the formula

Substitute \( P_1 = 0.750 \, \text{atm} \), \( V_1 = 3.50 \, \text{L} \), and \( P_2 = 1.50 \, \text{atm} \) into the formula:
\( V_2=\frac{0.750 \, \text{atm} \times 3.50 \, \text{L}}{1.50 \, \text{atm}} \)

Step5: Calculate the value of \( V_2 \)

First, calculate the numerator: \( 0.750\times3.50 = 2.625 \)
Then, divide by the denominator: \( V_2=\frac{2.625}{1.50}= 1.75 \, \text{L} \)

Answer:

\( 1.75 \, \text{L} \) (corresponding to the option "1.75 L")