Final answer:
To find the pressure of 1 mol of gas in a 5 L vessel at 77°C, convert the temperature to Kelvin and use the ideal gas law (PV = nRT). The calculated pressure is approximately 5.785 atm.
Step-by-step explanation:
To calculate the pressure of 1 mol of gas compressed into a 5 L vessel at 77°C, we can use the ideal gas law, which is expressed as PV = nRT. Here, P is the pressure we want to find, V is the volume of the gas (5 L), n is the number of moles (1 mol), R is the ideal gas constant (0.08206 L-atm/mol-K), and T is the temperature in Kelvin.
First, we need to convert the Celsius temperature to Kelvin:
T(K) = 77°C + 273.15 = 350.15 K.
Then we can plug in the values into the ideal gas law and solve for P:
PV = nRT
P = (nRT) / V
P = (1 mol * 0.08206 L-atm/mol-K * 350.15 K) / 5 L
P = 5.785 atm
Therefore, the pressure of the gas in the 5 L vessel at 77°C is approximately 5.785 atm.