what is the final volume of a 400.0mL gas sample that is subjected to a temperature change from 22.0 C to 30.0 C and a pressure change from standard pressure to 360.0 mm Hg

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what is the final volume of a 400.0mL gas sample that is subjected to a temperature change from 22.0 C to 30.0 C and a pressure change from standard pressure to 360.0 mm Hg

Given:

P_{1} = \text{760.0 mmHg}

T_{1} = \text{22.0°C + 273.15 = 295.15 K}

V_{1} = \text{400.0 mL}

P_{2} = \text{360.0 mmHg}

T_{2} = \text{30.0°C + 273.15 = 303.15 K}

Unknown:

V_{2}

Solution:

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

V_{2} = V_{1} × \frac{P_{1}}{P_{2}} × \frac{T_{2}}{T_{1}}

V_{2} = \text{400.0 mL} × \frac{\text{760.0 mmHg}}{\text{360.0 mmHg}} × \frac{\text{303.15 K}}{\text{295.15 K}}

\boxed{V_{2} = \text{867.3 mL}}

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