<h1>Problem</h1>
What is the pressure of 100 kg of nitrogen (<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>N</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">N_2</annotation></semantics></math>N2​) at 70°C in a 100 <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>m</mi><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">m^3</annotation></semantics></math>m3 tank in kilopascals? Round answer to the nearest kilopascal.
<h1>Solution</h1>
We can estimate the pressure using the ideal gas law:
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>P</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mi>R</mi><mi>T</mi></mrow><mi>V</mi></mfrac><mo>=</mo><mfrac><mrow><mo stretchy="false">(</mo><mn>100</mn><mo separator="true">,</mo><mn>000</mn><mi>g</mi><mtext> </mtext><msub><mi>N</mi><mn>2</mn></msub><mo>∗</mo><mo stretchy="false">(</mo><mfrac><mrow><mn>1</mn><mi>m</mi><mi>o</mi><mi>l</mi></mrow><mrow><mn>28</mn><mi>g</mi></mrow></mfrac><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>8.31446</mn><mfrac><mrow><msup><mi>m</mi><mn>3</mn></msup><mo>⋅</mo><mi>P</mi><mi>a</mi></mrow><mrow><mi>K</mi><mo>⋅</mo><mi>m</mi><mi>o</mi><mi>l</mi></mrow></mfrac><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>343</mn><mi>K</mi><mo stretchy="false">)</mo></mrow><mrow><mn>100</mn><msup><mi>m</mi><mn>3</mn></msup></mrow></mfrac><mo>≃</mo><mn>101842</mn><mtext> </mtext><mi>P</mi><mi>a</mi><mo>≃</mo><mn>102</mn><mtext> </mtext><mi>k</mi><mi>P</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">P = \frac{nRT}{V} = \frac{(100,000g \: N_2 * (\frac{1 mol}{28 g}))(8.31446 \frac{m^3 \cdot Pa}{K \cdot mol})(343 K)}{100 m^3} \simeq 101842 \: Pa \simeq 102 \: kPa</annotation></semantics></math>P=VnRT​=100m3(100,000gN2​∗(28g1mol​))(8.31446K⋅molm3⋅Pa​)(343K)​≃101842Pa≃102kPa</div>

Pressure of Gas in a Tank