The correct relationship between the molar mass of a gas, its temperature, and its pressure is given by the equation M = dRT/P, where M represents the molar mass of the gas, d is the density of the gas, R is the ideal gas constant, T is the temperature of the gas in Kelvin, and P is the pressure of the gas.

Explanation:

The molar mass of a gas is the mass of one mole of that gas. It is usually expressed in grams per mole (g/mol). The molar mass of a gas can be calculated by knowing the density of the gas, the ideal gas constant, the temperature of the gas, and the pressure of the gas.

- Equation M = dRT/P:
- M: Molar mass of the gas
- d: Density of the gas
- R: Ideal gas constant (8.314 J/(mol·K))
- T: Temperature of the gas in Kelvin
- P: Pressure of the gas

- Equation derivation:
- The ideal gas law equation, PV = nRT, relates the pressure (P), volume (V), amount of substance (n), ideal gas constant (R), and temperature (T) of a gas.
- By rearranging the ideal gas law equation, we can isolate the density (d) of the gas, which is defined as mass (m) divided by volume (V): d = m/V.
- Rewriting the equation in terms of density, we have P = (m/V)RT.
- Since the molar mass (M) is equal to the mass (m) divided by the amount of substance (n), we can substitute m/n with M in the equation: P = (M/nV)RT.
- The amount of substance (n) can be expressed as n = m/M, where m is the mass of the gas. Substituting n in the equation, we have P = (M/mV)RT.
- Finally, rearranging the equation, we get M = (dRT)/P, where d = m/V is the density of the gas.

Conclusion:
The correct relationship between the molar mass of a gas, its temperature, and its pressure is given by the equation M = dRT/P. This equation allows us to calculate the molar mass of a gas given its density, temperature, and pressure.