The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 kgm-3.
The root mean square speed of the gas molecules at that temperature is 602 ms-1. Assuming2
that the rate of diffusion of a gas is inversely proportional to the square root of its density,
calculate the density of the gas standard temperature and pressure if its root mean square
speed at is 490 ms-1
To calculate the density of the gas at standard temperature and pressure (STP) when its root mean square speed is 490 m/s, we can use the concept of the rate of diffusion being inversely proportional to the square root of its density.
Let's denote the density at STP as ρ_stp.
The rate of diffusion (R) can be expressed as:
R ∝ 1/√ρ
where ρ is the density.
From the given information, we know:
Density of gas at a certain temperature (ρ1) = 0.90 kg/m^3
Root mean square speed at that temperature (v1) = 602 m/s
Now we need to find the density at STP when the root mean square speed (v2) is 490 m/s.
Using the proportionality relationship, we can write:
R1 * √ρ1 = R2 * √ρ_stp
Substituting the given values:
(1/√ρ1) * √ρ1 = (1/√ρ_stp) * √ρ_stp
The left side of the equation becomes 1 since √ρ1 / √ρ1 = 1.
Thus, we have:
1 = (1/√ρ_stp) * √ρ_stp
Now, we can cancel out the square root terms:
1 = (√ρ_stp / √ρ_stp)
This simplifies to:
1 = 1
From this, we can conclude that the density at STP (ρ_stp) is equal to the density at a certain temperature (ρ1). So, the density of the gas at STP is 0.90 kg/m^3.