# An unknown gas shows a density of 2.4 g per litre at 273 deg C and 1140 mm Hg pressure.What is the gram molecular mass of the gas?

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If you can not use the ideal gas law I am guessing there is one more fact you left out. The volume of one mole of any gas at standard temperature and pressure is 22.4 liters. Given this fact you can use Charles' Law and Boyle's Law to get the molar mass.

Using Charles' Law you first need to find the volume of one liter of your gas given at standard temperature (273 K or 0 deg C).

V1/T1 = V2/T2

V1 = 1 liter T1 = 546 K (given as 273 C)

V2 = ? and T2 = 273 K (standard temperature)

Solving for V2:

V2 = (V1 * T2)/T1 = (1 liter * 273 K)/546 K = 0.5 liters

So far, the 2.4 grams that fit into 1 liter (from your given density) will fit into a 0.5 liter container if we cut the temperature in half (going from 546 K to 273 K). Next we have to figure out what changing the pressure will do.

Using Boyle's Law

P1 * V1 = P2 * V2

P1 = 1140 mm Hg V1 = 0.5 liters (answer from above)

P2 = 760 mm Hg (standard pressure) V2 = ?

Solve for V2

V2 = (P1 * V1)/P2 = (1140 mm Hg * 0.5 liters)/760 mm Hg

V2 = .75 liters

That means, the 2.4 grams that fit into the 1 liter container under the conditions given will fit int a 0.75 liter container at STP (standard temperature and pressure). Since 1 moles of any gas will occupy 22.4 liters at STP you can use proportions to show you only have .0335 moles of a gas.

x moles / 1 mole = 0.75 liters / 22.4 liters

solve for x to get .0335 moles.

Remeber that the original mass will not change so, the .0335 moles of gas has a mass of 2.4 grams.

2.4 grams /.0335 moles = 71.6 grams/mole

i am surprised to see a Class X standard student studying XII grade question.

This is the only way to find the unknown gas..

here we should know something about Ideal gas first..

Ideal gas :- is a hypothetical gas whose molecules occupy negligible space and have no interactions, and that consequently obeys the gas laws exactly. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces

Gas constant:- or ideal gas constant the constant is also combination of the constants from boyle's law, charles law, avogadro laws and gay-lussacs law. At standard condition that is at STP we will get gas constant value as It is equal to 8.314 joule kelvin-1 mole-1

(Value depend upon the units)

When we study an ideal gas and using all the laws under continues derivation we will get

PV=nRT

This is the only ideal gas using equation using which we can find the unknown gas, i am sorry there is no alternative way...

Given

Density (D) = 2.4 g/lts

Temperature (t) = 273ºC = 546 K

Pressure (p) = 1140 mmHg = 1.5 atm

Volume (V) = 1 lts.

Gas constant (R) = 0.082 L*atm/K*mol

Molar mass (M) = ?

First we have to find the mass from the given density.

D = 2.4 g/lts

Density = mass/volume

2.4 = mass/1 Lts

Mass (m) = 2.4 gm.

We know

PV = nRT

PV = (m/M)RT

1.5 * 1 = (2.4/M) 0.082 * 546

1.5 * M = 2.4 * 0.082 * 546

M = 107.45/1.5

M = 71.6

Molar mass = 71.6 which is almost equal to the molar mass of Germanium

Germanium is the unknown substance.