Question

If 253.0 mL of a gas at 842.30 mmHg and 39.1°C is heated in a flexible container, and the final pressure ismeasured at 162.40 mmHg with an expanded volume of 795.0 mL, what is the final temperature of this gasin degrees Celsius?-83.9-68.8189221

Answer 1

1) List the known quantities.

Sample: gas.

Volume 1: 253.0 mL.

Pressure 1: 842.30 mmHg.

Temperature 1: 39.1 ºC.

Pressure 2: 162.40 mmHg.

Volume 2: 795.0 mL

Temperature 2: unknown.

2) Convert units.

2.1- Convert ºC to K.

`K=ºC+273.15`
`K=39.1\text{ }ºC+273.15=312.25\text{ }K`

2.2- Convert mmHg to atm

1 atm = 760 mmHg

`atm=842.30\text{ }mmHg*\frac{1\text{ }atm}{760\text{ }mmHg}=1.1083\text{ }atm`
`atm=162.40\text{ }mmHg*\frac{1\text{ }atm}{760\text{ }mmHg}=0.21368\text{ }atm`

3) Set the equation.

`(P1V1)/(T1)=(P2V2)/(T2)`

4) Plug in the known quantities and solve for T2.

`T2=(P2V2T1)/(P1V1)`
`T2=\frac{(0.21368\text{ }atm)(0.7950\text{ }L)(312.25\text{ }K)}{(1.1083\text{ }atm)(0.2530\text{ }L)}`
`T2=189.17\text{ }K`

5) Convert K to ºC.

`ºC=K-273.15`
`ºC=189.17\text{ }K-273.15`
`ºC=-83.9\text{ }ºC`

The final temperature is -83.9 ºC.

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