Question

a sample of gas occupies 2.5 liters at a pressure of 1.2 atm and a temperature of 298.15 k. if the pressure is increased to 2.0 atm and the temperature is decreased to 283.15 k, what will be the new volume of the gas?
round to 3 sig figs. do not include units.
answer

Explanation:

Step1: Use the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\). We need to solve for \(V_2\).

Step2: Rearrange the formula for \(V_2\)

\(V_2=\frac{P_1V_1T_2}{P_2T_1}\)

Step3: Substitute the given values

Given \(P_1 = 1.2\), \(V_1=2.5\), \(T_1 = 298.15\), \(P_2 = 2.0\), \(T_2=283.15\)
\(V_2=\frac{1.2\times2.5\times283.15}{2.0\times298.15}\)

Step4: Calculate the value

First, calculate the numerator: \(1.2\times2.5\times283.15 = 849.45\)
Then, calculate the denominator: \(2.0\times298.15=596.3\)
\(V_2=\frac{849.45}{596.3}\approx1.42\)

Answer:

\(1.42\)