Question

what percent of sample of Nitrogen must be allowed to escape if its temperature pressure and volume are to be changed from 220 degree Celsius 3atm and 1.65litre to 110 degree Celsius 0.7 ATM and 1 litre respectively

Answer 1

Answer: $82\%$ sample of nitrogen must be allowed to escape if its temperature pressure and volume are to be changed from 220 degree Celsius 3 atm and 1.65 litre to 110 degree Celsius 0.7 atm and 1 litre respectively

Explanation:

The data given is as follows.

$P_{1}$ = 3 atm,   $V_{1}$ = 1.65 L, and $T_{1}$ = 220 + 273K = 493 K.

$P_{2}$ = 0.7 atm, $V_{2}$ = 1 L, and $T_{2}$ = 110 + 273 K = 383 K.

According to the ideal gas equation,      

                                  P V= n R T

or                           n = $\frac{P V}{R T}$

Using the above formula, calculate the value of $n_{1}$ as follows.

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

                                = $\frac{3 atm \times 1.65 L}{(0.082 L atm/mol K)\times 493 K}$

                                = 0.122

Similarly, calculate the value of $n_{2}$ as follows.

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

                               = $\frac{0.7 atm \times 1 L}{(0.082 L atm/mol K)\times 383 K}$

                                  = 0.022

Calculate fraction of moles as follows.

              Fraction of moles = $\frac {n_{2}}{n_{1}}$

                                            = $\frac {0.022}{0.122}$

                                            = 0.18

       $\%$ of fraction of moles = $0.18 \times 100$

                                                             = $18\%$

The percent of sample of nitrogen = $(100 - 18)\%$

                                                         = $82\%$

Thus, $82\%$ sample of nitrogen must be allowed to escape if its temperature pressure and volume are to be changed from 220 degree Celsius 3 atm and 1.65 litre to 110 degree Celsius 0.7 atm and 1 litre respectively.

Answer 2

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