13.6 Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 at a temperature of 27 °C and 1 atm pressure.
The ideal gas equation relating to pressure (P), volume (V) and absolute temperature (T) can be written as
PV = NT, where is Boltzmann constant = 1.38
N is the number of air molecules in the room.
N = = = 6.117
<p><strong>13.6 </strong>Volume of the room, V = 25.0 <span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math></span></p><p>Temperature of the room, T = 27 <span title="Click to copy mathml"><math><mi>? </mi></math></span> = 300 K</p><p>Pressure of the room, P = 1 atm = 1 <span title="Click to copy mathml"><math><mo>×</mo></math></span> 1.013 <span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>5</mn></mrow></mrow></msup></math></span> Pa</p><p>The ideal gas equation relating to pressure (P), volume (V) and absolute temperature (T) can be written as</p><p>PV = <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>k</mi></mrow></mrow><mrow><mrow><mi>B</mi></mrow></mrow></msub></math></span> NT, where <span title="Click to copy mathml"><math><msub><mrow><mrow><mi>k</mi></mrow></mrow><mrow><mrow><mi>B</mi></mrow></mrow></msub></math></span> is Boltzmann constant = 1.38 <span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>23</mn></mrow></mrow></msup></math></span> <span title="Click to copy mathml"><math><msup><mrow><mrow><mi>m</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup><mi>k</mi><mi>g</mi><msup><mrow><mrow><mi>s</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>2</mn></mrow></mrow></msup><msup><mrow><mrow><mi>K</mi></mrow></mrow><mrow><mrow><mo>-</mo><mn>1</mn></mrow></mrow></msup></math></span></p><p>N is the number of air molecules in the room.</p><p>N = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>P</mi><mi>V</mi></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>k</mi></mrow></mrow><mrow><mrow><mi>B</mi></mrow></mrow></msub><mi>T</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn><mi mathvariant="normal"></mi><mo>×</mo><mn>1.013</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>5</mn></mrow></mrow></msup><mo>×</mo><mn>25</mn></mrow></mrow><mrow><mrow><mn>1.38</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>23</mn></mrow></mrow></msup><mo>×</mo><mn>300</mn></mrow></mrow></mfrac></math></span> = 6.117 <span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>26</mn></mrow></mrow></msup></math></span></p>
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