According to the ideal gas law, the relationship between the pressure, volume, and temperature of a gas is given by the equation PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature of the gas in Kelvin.
If we have 2.9 L of gas at a pressure of 5.0 atm and a temperature of 50.0 °C, we can calculate the temperature of the gas if we decrease the volume of the gas to 2.4 and decrease the pressure to 3.0 atm by rearranging the ideal gas law equation as follows:
T = (PV) / (nR)
In this equation, T represents the temperature of the gas, P represents the pressure of the gas, V represents the volume of the gas, n represents the number of moles of gas, and R represents the ideal gas constant.
Plugging in the values from the problem into the equation, we get:
T = (5.0 atm * 2.9 L) / (n * 0.08206 L*atm / mol*K)
T = (14.5 L*atm) / (n * 0.08206 L*atm / mol*K)
T = (14.5 L*atm) / (n * 0.08206 L*atm / mol*K)
T = 177.2 K
Therefore, if we have 2.9 L of gas at a pressure of 5.0 atm and a temperature of 50.0 °C, and we decrease the volume of the gas to 2.4 and decrease the pressure to 3.0 atm, the temperature of the gas will be 177.2 K.