Question

a gas at 5.00 atm pressure was stored in a tank during the winter at 5.0 °c. during the summer, the temperature in the storage area reached 40.0 °c. what was the pressure in the gas tank in the summer? 5.63 atm 0.625 atm 4.44 atm 40.0 atm 69.5 atm

Explanation:

Step1: Convert temperatures to Kelvin

For winter: \(T_1 = 5.0+273.15=278.15\space K\)
For summer: \(T_2 = 40.0 + 273.15=313.15\space K\)

Step2: Apply Gay - Lussac's Law (\(P_1/T_1=P_2/T_2\))

We know \(P_1 = 5.00\space atm\), \(T_1 = 278.15\space K\), \(T_2=313.15\space K\). Rearranging for \(P_2\) gives \(P_2=\frac{P_1T_2}{T_1}\)
Substitute values: \(P_2=\frac{5.00\times313.15}{278.15}\)
Calculate: \(P_2=\frac{1565.75}{278.15}\approx5.63\space atm\)

Answer:

5.63 atm