QuestionA flexible vessel contains 37 L of gas where the pressure is 1.0 atm . What will the volume be when the pressure is 0.70 atm , the temperature remaining constant? a. 0.019 L b. 37 L c. 53 L d. 0.046 L e. 26 L

Studdy Solution

STEP 1

1. The initial volume of the gas is 37 L.
2. The initial pressure of the gas is 1.0 atm.
3. The final pressure of the gas is 0.70 atm.
4. The temperature of the gas remains constant.
5. We are using Boyle's Law, which states that $P_1V_1 = P_2V_2$ for a given mass of gas at constant temperature.
6. We need to find the final volume of the gas.

STEP 2

1. Identify the known variables and the unknown variable.
2. Write the equation based on Boyle's Law.
3. Solve for the unknown variable (final volume).

STEP 3

Identify the known variables and the unknown variable.
- Initial volume, $V_1 = 37 \, \text{L}$ - Initial pressure, $P_1 = 1.0 \, \text{atm}$ - Final pressure, $P_2 = 0.70 \, \text{atm}$ - Final volume, $V_2 = ?$

STEP 4

Write the equation based on Boyle's Law.
According to Boyle's Law: $P_1V_1 = P_2V_2$
Substitute the known values into the equation: $1.0 \times 37 = 0.70 \times V_2$

STEP 5

Solve for the unknown variable (final volume).
Rearrange the equation to solve for $V_2$ : $V_2 = \frac{1.0 \times 37}{0.70}$
Calculate $V_2$ : $V_2 = \frac{37}{0.70}$ $V_2 = 52.857$
Round to the nearest whole number, since the options are given in whole numbers: $V_2 \approx 53 \, \text{L}$
Thus, the final volume of the gas is: $\boxed{53 \, \text{L}}$

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