Question

at a given volume and temperature the presure of a gas will vary 1.directly proprtional to the mass of a gas 2.inversely proportional to mass of gas 3.linearly as the square of the mass of the gas 4.inversely as the square of the mass. please explain your answer

Answer 1

The ideal gas law is given as PV=nRT where
 P = pressure
V = volume
n = number of moles of gas
R = a constant
T = temperature

Given that V and T are constant. So P is directly proportional to n.
Since mass of the gas is directly proportional to number of moles of gas, Pressure will vary directly proportional to mass of gas.

Answer is (1).

Answer 2

The ideal gas law states that :

        P * V = n R T

Volume and temperature are given.  Then the pressure will vary as:
       P = RT/V  * n

 n is the number of moles of the gas present in the vessel/container.

       n = m/M  where  m = mass of the gas in the container and
                               M is the molar mass of the gas - which is fixed.

     P = RT/(VM)  * m

Hence, the pressure is directly proportional to the mass of the gas.