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ANSWER
The final pressure of the gas is 1350.22 mmHg
STEP-BY-STEP EXPLANATION:
Given information
[tex]\begin{gathered} \text{The initial volume of the gas = 500 cm}^3 \\ \text{ Initial temperature = 27}\degree C \\ \text{ Initial pressure = 900 mmHg} \\ \text{ Final temperature = -48}\degree C \\ \text{ Final volume = }250cm^3 \end{gathered}[/tex]From the question provided, you were asked to find the final pressure of the gas, hence, we assume that x represents the final pressure of the gas
To find the final pressure of the gas, we need to apply the general gas law
[tex]\frac{P1V1}{T1}\text{ = }\frac{P2V2}{T2}[/tex]Where,
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
The next process is to convert the final and initial temperature from degree Celcius to degree kelvin
[tex]\begin{gathered} T\degree K\text{ = T}\degree C\text{ + 273.15} \\ T1\text{ = 27 + 273.15} \\ T1\text{ = 300.15K} \\ T2\text{ = -48 + 273.15} \\ T2\text{ = 225.15K} \end{gathered}[/tex]The next thing is to substitute the given data into the above formula
[tex]\begin{gathered} \frac{P1V1}{T1}\text{ = }\frac{P2V2}{T2} \\ \\ \frac{900\cdot\text{ 500}}{300.15}\text{ = }\frac{x\cdot\text{ 250}}{225.15} \\ \frac{450000}{300.15}\text{ = }\frac{250x}{225.15} \\ Cross\text{ multiply} \\ 300.15\cdot\text{ 250x = 450000 }\cdot\text{ 225.15} \\ 75037.5x\text{ = 101317500} \\ \text{Divide both sides 75027.5} \\ \frac{75037.5x}{75037.5}\text{ = }\frac{101317500}{75037.5} \\ x\text{ = 1350.22 mmHg} \end{gathered}[/tex]Therefore, the final pressure of the gas is 1350.22 mmHg
