Question

A sample of a gas has a pressure of 82.5 kPa in a 300 cm3 container at 25°C. At what temperature in Celsius the pressure will be 400 torr if the gas is transferred to a container 500 cm3?

every time i use V1P1 V2P2 law
----------- -----------
T1 T2

i keep getting 1806 but my book says 321K?

Answer 1

what grade is this

Answer 2

My guess is a mistake in units somewhere. Two things to note: for ideal gas formulas, the temperature needs to be in Kelvin. Kelvin, unlike Celcius, is directly proportional to internal energy. Therefore, for proportional relationships like this, temperature needs to be in Kelvin.

To go from Celsius to Kelvin, add 273.15.

Second thing, the two pressures are given in different units. One in kPa, the other in torr.

Relevant conversion factors to know/memorize: 1 atm = 760 torr = 760 mmHg = 101.3 kPa

Both pressures need to be in the same unit to work. For my own calculations, I decided to convert the second pressure to kPa.

\[\frac{ 400~torr }{ }\frac{ 1~atm }{ 760~torr }\frac{ 101.3~kPa }{ 1~atm }=53.32~kPa\]

so plugging everything in

(300cm^3)(82.5kPa) / (25 + 273.15) = (500 cm^3)(53.32 kPa)/(x K)

I was able to get the answer stated in your textbook.