What is the pressure exerted by 4.5m\(^3\) of gas at 17ºC in a cylinder if the number of moles is 8.3 moles? (R = 8.31 JK\(^{-1}\)mol\(^{-1}\))
A
3170Pa
B
6740Pa
C
2850Pa
D
4445Pa
Verified Correct Answer: D.
Physical Principles & Numerical Solution
The ideal gas law is \( PV = nRT \).
Making \( P \) the subject:
\[ P = \frac{nRT}{V} \]
Substitute the values:
- \( n = 8.3 \, \mathrm{mol} \), \( R = 8.31 \, \mathrm{J \, K^{-1} \, mol^{-1}} \), \( T = 17^\circ \mathrm{C} = 290 \, \mathrm{K} \)
- \( V = 4.5 \, \mathrm{m}^3 \)
\( P = \frac{8.3 \times 8.31 \times 290}{4.5} = 4444.93 \, \mathrm{Pa} \)
Source: Myschool Past Questions Archive (Record #74432)