Question

The pressure of a gas which occupies 500cm3 at27°C is 900 mm Hy. what is the pressure of thegasat -48°c if thethe volume is reduced to250cm3 ?

Answer 1

The final pressure of the gas is 1350.22 mmHg

Explanation:

Given information

`\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}`

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

`(P1V1)/(T1)\text{ = }(P2V2)/(T2)`

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

`\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}`

The next thing is to substitute the given data into the above formula

`\begin{gathered} (P1V1)/(T1)\text{ = }(P2V2)/(T2) \\ \\ \frac{900\cdot\text{ 500}}{300.15}\text{ = }\frac{x\cdot\text{ 250}}{225.15} \\ (450000)/(300.15)\text{ = }(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} \\ (75037.5x)/(75037.5)\text{ = }(101317500)/(75037.5) \\ x\text{ = 1350.22 mmHg} \end{gathered}`

Therefore, the final pressure of the gas is 1350.22 mmHg