The pressure of the gas is 2700 mmHg.
To solve this problem, we can use the Combined Gas Laws:
(p_1V_1)/T_1 = (p_2V_2)/T_2
p_2 = p_1 × V_1/V_2 × T_2/T_1
T_2 = (-55+273.15) K = 218.15 K; T_1 = (33+273.15) K = 306.15 K
p2 = 760 mmHg × (0.50 m^3/0.10 m^3) × (218.15 K/306.15 K) = 2700 mmHg
Answer:
The pressure of the gas at these new conditions is 2700 mmHg.
Explanation:
Data:
initial pressure, P1 = 760 mmHg
initial volume, V1 = 0.5 m^3
initial temperature, T1 = 33 + 273 = 306 K
final pressure, P2 = ? mmHg
final volume, V2 = 0.1 m^3
final temperature, T2 = -55 + 273 = 218 K
Using the Combined gas law we get:
P1*V1/T1 = P2*V2/T2
Solving for P2 and replacing with data (dimensions are omitted):
P2 = P1*V1*T2/(T1*V2)
P2 = 760*0.5*218/(306*0.1)
P2 ≈ 2700 mmHg
