Question

a sample of gas occupies 3.5 liters at a pressure of 1.3 atm and a temperature of 298.15 k. if the pressure is increased to 2.8 atm and the temperature is decreased to 273.15 k, what will be the new volume of the gas?
a 1.49 l
b 1.77 l
c 2.98 l
d 0.000156 l

Explanation:

Step1: Recall the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 1.3\) atm, \(V_1=3.5\) L, \(T_1 = 298.15\) K, \(P_2 = 2.8\) atm, \(T_2=273.15\) K, and \(V_2\) is the unknown.

Step2: Solve for \(V_2\)

Rearrange the formula for \(V_2\): \(V_2=\frac{P_1V_1T_2}{P_2T_1}\).
Substitute the values: \(V_2=\frac{1.3\times3.5\times273.15}{2.8\times298.15}\).
First, calculate the numerator: \(1.3\times3.5\times273.15 = 1.3\times956.025=1242.8325\).
Then, calculate the denominator: \(2.8\times298.15 = 834.82\).
Now, \(V_2=\frac{1242.8325}{834.82}\approx1.49\) L.

Answer:

A. 1.49 L