Question

One litre of a gas is at a pressure of 10 _6 mm of Hg at 250c. How many molecules are present in the vessel ? (a) 3.2 x.106 (b) 3.2 x 10 13 (c) 3.2 x 1010 (d) 3 x 104​

Answer 1

GIVEN:-

$\bf \: pressure(p _{1}) = 10 {}^{ - 6} mm \: of \: hg \: and \: volume(v _{1}) = 1litre$

$\bf \: temperature \: in \: c {}^{0}(t _{ 2 }) = 25 {}^{0} c = (273 + 25)k = 298k(t _{1})$

TO FIND OUT:-

$\bf \: number \: of \: molecules \: present \: in \: vessel = {?}$

SOLUTION:-

$\bf \: we \: know \: that \: 760 \: mm \: of \: hg = 1atm$

$\therefore \bf \: p _{2} = 760mm \: of \: hg$

$\bf \: now \: \large\frac{p _{1}v _{1}}{t _{1} } = \frac{p _{2} \times v _{2}}{t _{2} }$

$\bf \implies \large \frac{10 {}^{ - 6} \times 1000}{298} = \frac{760 \times v _{2}}{273}$

$\bf \implies \: v _{2} = 1.2 \times 10 {}^{ - 6} cc(at \: stp)$

$\bf \: number \: of \: molecules = \large \frac{6.02 \times 10 {}^{26} }{22400} \times \small1.2 \times 10 {}^{ - 6}$

$\boxed{ \bf \implies \: 3.2 \times 10 {}^{13} }$

$\bf \: so \: the \: correct \:option \: is \: b(3.2 \times 10 {}^{13} )$