Final answer:
The relationship between the mass of a gas at constant temperature and the pressure-volume product is an inverse relationship by Boyle's law, which states that at constant temperature, the product of pressure and volume of a given mass of gas remains constant.
Step-by-step explanation:
The relationship between the mass of a gas at a constant temperature (denoted by p) and the pressure-volume product (denoted by b) can be understood by exploring Boyle's law, which states that the pressure-volume product of a gas is a constant when the temperature is constant. Considering that p represents mass density and b is the product of pressure and volume (PV), the directly proportional relationship describes that as pressure increases, volume decreases to maintain the constant PV product, which is essentially the mass of the gas assuming constant density.
Boyle's Law is represented mathematically as P₁V₁ = P₂V₂, where P and V are the pressure and volume of the gas, respectively. Thus for a given gas at constant temperature, the relationship between p and b can be described in that doubling the pressure would result in halving the volume if the mass (and thus density) of the gas remains constant. This inverse relationship holds true as long as the mass (m), temperature (T), and amount of gas (in moles, n) remain constant; allowing us to understand how pressure and volume interact under these conditions.