To solve this problem, we can use the ideal gas law, which states that the product of pressure and volume is directly proportional to the product of the number of moles, the gas constant, and the temperature of a gas. The equation for the ideal gas law is:
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 (0.0821 L·atm/(mol·K)) T is the temperature of the gas in Kelvin
We can rearrange the ideal gas law equation to solve for temperature:
T = PV / (nR)
In this case, we can assume that the number of moles, volume, and gas constant remain constant. Therefore, we can write:
T1 = P1V / (nR) T2 = P2V / (nR)
We can now find the new temperature (T2) by plugging in the given values:
T2 = (P2V) / (nR) = (1.19 ATM * V) / (n * R)
Since we are not given the volume or number of moles, we cannot determine the exact new temperature. However, if the volume and the number of moles remain constant, the new temperature (T2) can be expressed as:
T2 = (P2 / P1) * T1 = (1.19 ATM / 1.57 ATM) * 345K = 0.758 * 345K = 261.51K
Therefore, if the volume and the number of moles remain constant, the new temperature of the gas would be approximately 261.51 Kelvin.