It is found that an unknown gas has a density of 2.5 times that of Oxygen gas of the same Temperature and Pressure. What is its molecular weight?

It will be 2.5*32 = ?

The long way is to calculate the density of O2 (32g/22.4L = 1.43 g/L), multiply by 2.5 for a density of the unknown of 3.57 g/L, so 22.4L has a mass of 22.4*3.57 = 80 which is a mole.

To find the molecular weight of the unknown gas, we can use the concept of the Ideal Gas Law, which states that the product of pressure (P), volume (V), and the number of moles (n) of a gas is proportional to its temperature (T) and the universal gas constant (R).

The formula for the Ideal Gas Law is given as:
PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles
R = Universal gas constant
T = Temperature

In this case, we can assume that the volume, pressure, and temperature are constant for both the unknown gas and oxygen gas. Therefore, the ratio of their number of moles (n₁ and n₂) will be equal to their ratio of densities (ρ₁ and ρ₂).

Density is defined as the mass (m) of a substance divided by its volume (V). Therefore, the ratio of their densities can be expressed as:

ρ₁/ρ₂ = (m₁/V)/(m₂/V) = m₁/m₂

Where:
ρ₁ = Density of the unknown gas
ρ₂ = Density of oxygen gas
m₁ = Mass of the unknown gas
m₂ = Mass of oxygen gas

Given that the density of the unknown gas is 2.5 times that of oxygen gas, we can say:

ρ₁/ρ₂ = 2.5

Now, let's assume the molecular weight of the unknown gas is represented by M. The molecular weight of oxygen gas (O₂) is approximately 32 g/mol.

Using the formula for density, we can relate the molecular weights of the two gases as follows:

ρ = (m/V) = (M/n) = (M/V)(1/M) = ρ(M/M₂)

Where:
ρ = Density
M = Molecular weight of the unknown gas
M₂ = Molecular weight of oxygen gas

Since the density ratio is known (ρ₁/ρ₂ = 2.5), we can write:

2.5 = ρ₁/ρ₂ = (ρ(M/M₂))/(ρ₂) = M/M₂

Now, we can rearrange the equation to solve for the molecular weight of the unknown gas (M):

M = 2.5 * M₂

Substituting the known value for the molecular weight of oxygen gas (M₂ = 32 g/mol):

M = 2.5 * 32 = 80 g/mol

Therefore, the molecular weight of the unknown gas is 80 g/mol.