Question

a gas has an initial volume of 2.4 l at a pressure of 1.5 atm and a temperature of 273 k. the pressure of the gas increases to 4.5 atm, and the temperature of the gas increases to 313 k. what is the final volume of the gas? 0.70 l 0.92 l 6.3 l 8.3 l

Explanation:

Step1: Recall Combined Gas Law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\), where \(P_1 = 1.5\) atm, \(V_1 = 2.4\) L, \(T_1 = 273\) K, \(P_2 = 4.5\) atm, \(T_2 = 313\) K, and \(V_2\) is the final volume.

Step2: Rearrange Formula for \(V_2\)

Rearranging the combined gas law gives \(V_2=\frac{P_1V_1T_2}{P_2T_1}\).

Step3: Substitute Values

Substitute the given values: \(P_1 = 1.5\), \(V_1 = 2.4\), \(T_2 = 313\), \(P_2 = 4.5\), \(T_1 = 273\) into the formula.
\(V_2=\frac{1.5\times2.4\times313}{4.5\times273}\)
First, calculate the numerator: \(1.5\times2.4 = 3.6\); \(3.6\times313 = 1126.8\)
Then, calculate the denominator: \(4.5\times273 = 1228.5\)
Now, divide numerator by denominator: \(V_2=\frac{1126.8}{1228.5}\approx0.92\) L.

Answer:

0.92 L (corresponding to the option "0.92 L")