Question

A sample of gas with an initial volume of 28.4 Liters at a pressure of 725 mmHg and a temperature of 305 K is compressed to a volume of 14.8 Liters and warmed to a temperature of 375 Kelvin. What is the final pressure of the gas?

Answer 1

Answer:

The final pressure is 2.25 atm or 1710 mm Hg

Explanation:

Step 1: Data given

The initial volume = 28.4 L

The initial pressure = 725 mm Hg ( = 725/760 atm) = 0.953947 atm

The initial temperature = 305 K

The new volume is 14.8 L

The new temperature = 375 K

Step 2: Calculate the new pressure

(P1*V1)/T1 = (P2*V2)/T2

⇒ with P1 = the initial pressure = 725 mmHg = 0.953947 atm

⇒ with V1 = the initial volume = 28.4 L

⇒ with T1  = The initial temperature = 305 K

⇒ with P2 = the new pressure = TO BE DETERMINED

⇒ with V2 = the new volume = 14.8 L

⇒ with T2 = the new temperature = 375 K

(0.953947 * 28.4)/305 = (P2 * 14.8)/375

P2 = 2.25 atm = 1710 mm Hg

The final pressure is 2.25 atm or 1710 mm Hg

Answer 2

The final pressure of the gas is 1.71 * 10³ mmHg.

Based on the given information,  

• The initial volume of gas is 28.4 L.

• The initial pressure of the gas is 725 mmHg.

• The initial temperature given is 305 K.  

• The final volume of the gas is 14.8 L.

• The final temperature given is 375 K.

Now the final pressure of the gas can be determined using ideal gas equation,

$\frac{P1V1}{T1} =\frac{P2V2}{T2}$

$P2=\frac{P1V1}{T1} *\frac{T2}{V2}$

$P2=\frac{28.4L*725mmHg*375K}{305K*14.8L}$

$P2=\frac{7721250}{4514} mmHg$

$P2=1710.5117 mmHg$

$P2=1.71*10^{3} mmHg$

Thus, the final pressure of the gas is 1.71 * 10³ mmHg.

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