Answer: To determine the pressure change of a gas when it is heated at constant volume, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Since the volume of the gas is constant, we can simplify the equation to:
P/T = nR/V
The quantity nR/V is a constant, which means that P/T is also a constant at constant volume. Therefore, we can use the following equation to calculate the pressure at a new temperature:
P2/T2 = P1/T1
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
We can convert the temperatures to Kelvin by adding 273.15:
T1 = 30.0 °C + 273.15 = 303.15 K
T2 = 40.0 °C + 273.15 = 313.15 K
We can plug in the given values and solve for P2:
P2/313.15 K = 2.50 atm/303.15 K
P2 = (2.50 atm)(313.15 K)/(303.15 K)
P2 = 2.58 atm
Therefore, the pressure of the gas increases from 2.50 atm to 2.58 atm when it is heated from 30.0 °C to 40.0 °C at constant volume.
Step-by-step explanation: