Answer:
Explanation:
According to the ideal gas law, the pressure (P) and temperature (T) of a gas are related by the equation P = nRT/V, where n is the number of moles of gas, R is the ideal gas constant, and V is the volume of the gas.
Since the cylinders are identical and have the same pressure, we can assume that they have the same volume (V) and ideal gas constant (R). Therefore, the only difference between the two cylinders is the number of moles of gas (n) and the temperature (T).
Let's denote the number of moles of argon as n_ar and the number of moles of krypton as n_kr. We can express the ratio of the temperatures (T_ar and T_kr) as follows:
T_ar / T_kr = n_ar / n_kr
Since the cylinders contain the same mass of argon and krypton, we can use the molar mass (M) of each gas to relate the number of moles to the mass:
n_ar = mass_ar / M_ar
n_kr = mass_kr / M_kr
The molar mass of argon (M_ar) is approximately 39.95 g/mol, and the molar mass of krypton (M_kr) is approximately 83.80 g/mol.
Now, let's consider the ratio of the masses (mass_ar and mass_kr) of the gases in the cylinders:
mass_ar / mass_kr = M_ar / M_kr
Combining the above equations, we can simplify the ratio of the temperatures:
T_ar / T_kr = (mass_ar / M_ar) / (mass_kr / M_kr)
= (mass_ar / mass_kr) * (M_kr / M_ar)
= (M_kr / M_ar) * (mass_ar / mass_kr)
Therefore, the ratio of the temperatures (T_ar / T_kr) is equal to the ratio of the molar masses (M_kr / M_ar) multiplied by the ratio of the masses of the gases (mass_ar / mass_kr).
Note that this ratio assumes that the volumes and pressures are the same. If there are any other factors at play, such as a change in volume or pressure, this ratio may not hold true.