Question

21.7 ml of gas at 98.8 kpa is allowed to expand at constant temperature into a 52.7 ml container. what is the new pressure of the gas?
your answer should be rounded to three significant figures. do not include units in your answer.
____ kpa
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Explanation:

Step1: Apply Boyle's Law

Boyle's Law is \(P_1V_1 = P_2V_2\). Here, \(P_1 = 98.8\ \text{kPa}\), \(V_1=21.7\ \text{mL}\), and \(V_2 = 52.7\ \text{mL}\). We need to find \(P_2\).
From \(P_1V_1 = P_2V_2\), we can solve for \(P_2\) as \(P_2=\frac{P_1V_1}{V_2}\).

Step2: Substitute the values

Substitute \(P_1 = 98.8\), \(V_1 = 21.7\), and \(V_2=52.7\) into the formula:
\(P_2=\frac{98.8\times21.7}{52.7}\)
First, calculate the numerator: \(98.8\times21.7=(100 - 1.2)\times21.7=100\times21.7-1.2\times21.7=2170-26.04 = 2143.96\)
Then, \(P_2=\frac{2143.96}{52.7}\approx40.7\)

Answer:

\(40.7\)