Question

The density of gas at 100KPa is 0.1gdm-3.it's RMS speed will be​

Answer 1

Refer to the attachment for answer

Answer 2

The RMS speed of the gas is 1732 m/s

Explanation:

Assuming ideal gas behavior, the equation follows:

PV = nRT

We know that:

$\text{Density}=\frac{\text{Mass}}{\text{Volume}}$

Rearranging the above equation:

$M=\frac{dRT}{P}$

Or,

$\frac{d}{P}=\frac{M}{RT}$     .......(1)

The formula used for root mean square speed is:

$\nu_{rms}=\sqrt{\frac{3RT}{M}}$       .......(2)

Substituting relation 1 in equation 2, we get:

$\nu_{rms}=\sqrt{\frac{3P}{d}$

where,

$\nu_{rms}$ = root mean square speed

p = pressure of gas = 100 kPa = $10^5Nm^{-2}$     (Conversion factor:  $1kPa=1000Nm^{-2}$ )

d = density of gas = $0.1g/dm^3=0.1kg/m^3$      (Conversion factor:   $1g/dm^3=1kg/m^3$ )

Putting values in above equation, we get:

$\nu_{rms}=\sqrt{\frac{3\times 10^5N/m^2}{0.1kg/m^3}}\\\\\nu_{rms}=1.723\times 10^3m/s$

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