Question

the density of a gas is found to be 3.43 gm / l^3 at 300 k and 1 atm pressure . calculate the molar mass of the gas.......plzzzzz do it fast

Answer 1

d = 3.43 g/L^3
T = 300K
P = 1 atm

M = dRT / P
= (3.43 g/L^3 * 0.0821 L.atm/(mol K) * 300 K) / (1 atm)
= 84.48 g/mol

Molar mass of gas = 84.48 g/mol

Answer 2

Explanation:

It is known that density is mass present in per unit volume. Also, number of moles of a substance equals mass divided by molar mass.

Mathematically,     density = $\frac{mass}{volume}$   ....... (1)

and,          no. of moles = $\frac{mass}{\text{molar mass}}$ ...... (2)

Hence, equating the equations (1) and (2) we get the following.

                    V = $\frac{n \times M}{d}$  ...... (3)

Also, equation for ideal gas is PV = nRT.

Therefore, putting the given values and using equation (3) as follows.

                       PV = nRT

                    $P \frac{n \times M}{d} = nRT$

or,                $P \frac{M}{d} = RT$

                   $1 atm \times \frac{M}{3.43 gm/l^{3}} = 0.0821 atm L/mol K \times 300 K$

                          M = 84.48 $g/l^{2}$

Thus, we can conclude that molar mass of the gas is 84.48 $g/l^{2}$.