Question

if the density of oxygen is 1.44kg/m^3 at a pressure of 10^5N/m^2,find the root mean square velocity of oxygen molecule​

Answer 1

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$V_r_m_s=\:\:\sqrt{ \frac{3RT}{M}$

We know that PV = RT

So, $V_r_m_s = \:\:\sqrt{\frac{3PV}{M} }$

Now, when we take reciprocal of V and M, we get M/V, which is density

$\sqrt{\frac{3P}{\frac{M}{V} } }$

Given, density = 1.44

P = 10⁵

$V_r_m_s=\:\:\sqrt{\frac{3x10^5}{1.44} }$

Now, after simplification,

$V_r_m_s=\:\:\sqrt{2.083x10^5}$ = 456.45 = 456 m/s approx