Question

a cylinder is filled with 10.0 l of gas and a piston is put into it. the initial pressure of the gas is measured to be 237. kpa. the piston is now pulled up, expanding the gas, until the gas has a final volume of 68.0 l. calculate the final pressure of the gas. be sure your answer has the correct number of significant digits. piston cylinder gas kpa

Explanation:

Step1: Apply Boyle's Law

Boyle's Law states that \(P_1V_1 = P_2V_2\) (for a fixed amount of gas at constant temperature).
Given \(P_1 = 237\ \text{kPa}\), \(V_1=10.0\ \text{L}\), \(V_2 = 68.0\ \text{L}\). We need to solve for \(P_2\).
Rearrange the formula to \(P_2=\frac{P_1V_1}{V_2}\).

Step2: Substitute values

Substitute the values into the formula:
\(P_2=\frac{237\ \text{kPa}\times10.0\ \text{L}}{68.0\ \text{L}}\)
First, calculate \(237\times10.0 = 2370\).
Then, \(\frac{2370}{68.0}\approx34.9\) (using significant - digit rules. The least number of significant digits in the given values is 3, so the result should have 3 significant digits).

Answer:

\(34.9\ \text{kPa}\)