To find the temperature of an ideal gas, we can use the ideal gas equation:
PV=nRTwhere:
P is the pressure in atmospheres,
V is the volume in liters
(dm3),
n is the number of moles,
R is the gas constant
(0.0821dm3atmK−1mol−1), and
T is the temperature in Kelvin.
Given:
We can rearrange the ideal gas equation to solve for
T :
T=Plugging in the given values:
T=| (4.926atm)(20dm3) |
| (2mol)(0.0821dm3atmK−1mol−1) |
T=| 98.52atm⋅dm3 |
| 0.1642dm3atmmol−1 |
T=600KTo convert the temperature from Kelvin to Celsius, use the conversion formula:
Celsius = Kelvin −273.15For our calculation:
Celsius =600K−273.15 Celsius =326.85≈327∘CTherefore, the temperature of the gas in degree Celsius is closest to Option B: 327 .