A flask containing 10g of a Gas of relative molecular mass 100 at a pressure of 100kPa was evacuated to a pressure of 0.01 kPa at constant temperature. Which one of the following is the best estimate of the number of molecules left in the flask?

6.02X10¹⁶

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6.02X10¹⁷

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6.02X10¹⁸

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6.02X10¹⁹

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Solution

The correct option is C
6.02X10¹⁸

$\frac{P V}{n T} = R (c o n s t a n t)$

$\frac{P_{1} V_{1}}{n_{1} T_{1}} = \frac{P_{2} V_{2}}{n_{2} T_{2}}$

When, $V_{1} = V_{2} a n d T_{1} = T_{2}$
$∴ \frac{P_{1}}{n_{1}} = \frac{P_{2}}{n_{2}} \Rightarrow n_{2} = \frac{0.1 \times 0.01}{100}$
$n_{2} = 1 \times 10^{- 5}$
Number of molecules left = $n_{2} N$
$= 1 \times 10^{- 5} \times 6.02 \times 10^{23} = 6.02 \times 10^{18}$

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A flask containing 10g of a Gas of relative molecular mass 100 at a pressure of 100kPa was evacuated to a pressure of 0.01 kPa at constant temperature. Which one of the following is the best estimate of the number of molecules left in the flask?

The correct option is C 6.02X1018 PVnT=R(constant) P1V1n1T1=P2V2n2T2 When, V1=V2 and T1=T2 ∴P1n1=P2n2⇒n2=0.1×0.01100 n2=1×10−5 Number of molecules left = n2N =1×10−5×6.02×1023=6.02×1018