Question

a gas occupies a volume of 2.45 l at a pressure of 1.03 atm at a temperature of 300.0 k. what volume will the gas occupy if the pressure is changed to 0.980 atm and the temperature is changed to 335.5 k? which gas law equation should be used to solve this problem?

$$\frac { p _ { 1 } v _ { 1 } } { t _ { 1 } } = \frac { p _ { 2 } v _ { 2 } } { t _ { 2 } }$$

$$\frac { v _ { 1 } } { t _ { 1 } } = \frac { v _ { 2 } } { t _ { 2 } }$$

$$\frac { p _ { 1 } } { t _ { 1 } } = \frac { p _ { 2 } } { t _ { 2 } }$$

$$p _ { 1 } v _ { 1 } = p _ { 2 } v _ { 2 }$$

$$p v = n r t$$

$$\frac { v _ { 1 } } { n _ { 1 } } = \frac { v _ { 2 } } { n _ { 2 } }$$

solve for the unknown variable. l

Explanation:

Step1: Identify the gas law equation

Since the problem involves changes in pressure, volume, and temperature, the combined gas law $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$ is used.

Step2: Rearrange the formula to solve for \(V_2\)

$$
LATEXBLOCK0
$$

Step3: Substitute the given values

Given \(P_1 = 1.03\space atm\), \(V_1=2.45\space L\), \(T_1 = 300.0\space K\), \(P_2=0.980\space atm\), \(T_2 = 335.5\space K\)

$$
LATEXBLOCK1
$$

First, calculate \(1.03\times2.45 = 2.5235\)
Then \(2.5235\times335.5=846.63425\)
Finally, \(V_2=\frac{846.63425}{294}\approx 2.88\space L\)

Answer:

The gas law equation is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\) and the volume \(V_2\) is \(2.88\space L\)