Question

The volume of a gas at 27°C and 700.0 mmHg is 600.0 mL.What is the volume of the gas at 20.0°C and 500.0 mmHg

Answer 1

Hello!

The volume of a gas at 27 ºC and 700.0 mmHg is 600.0 mL. What is the volume of the gas at 20.0 ºC and 500.0 mmHg ?

We have the following information:

T1 (initial temperature) = 27 ºC (in Kelvin)

TK = TC+273.15 → TK = 27+273.15 → TK = 300.15

T1 (initial temperature) = 300.15 K

P1 (initial pressure) = 700.0 mmHg

V1 (initial volume) = 600.0 mL

V2 (final volume) = ? (in mL)

T2 (final temperature) = 20 ºC (in Kelvin)

TK = TC+273.15 → TK = 20+273.15 → TK = 293.15

T2 (final temperature) = 293.15 K

P2 (final pressure) = 500.0 mmHg

Now, we apply the data of the variables above to the General Equation of Gases, let's see:

$\dfrac{P_1*V_1}{T_1} = \dfrac{P_2*V_2}{T_2}$

$\dfrac{700.0*600.0}{300.15} = \dfrac{500.0*V_2}{293.15}$

$\dfrac{420000}{300.15} = \dfrac{500.0\:V_2}{293.15}$

multiply the means by the extremes

$300.15*500.0\:V_2 = 420000*293.15$

$150075\:V_2 = 123123000$

$V_2 = \dfrac{123123000}{150075}$

$\boxed{\boxed{V_2 \approx 820.4\:mL}}\:\:\:\:\:\:\bf\blue{\checkmark}\bf\green{\checkmark}\bf\red{\checkmark}$

Answer:

The volume is approximately 820.4 mL

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Answer 2

Answer:

The unknown volume is 820.4ml

Explanation:

Given data is

Initial Parameters

Volume of gas=600ml

Pressure if gas=700mm of Hg

Temperature of gas=27°C=300K

Final Parameters

Volume of gas=?

Pressure if gas=500mm of Hg

Temperature of gas=20°C=293K

To find the unknown volume,we use the following relation

$\frac{ P_{1}V_{1} }{T _{1}} = \frac{ P_{2}V_{2} }{T _{2}}$

Therefore by substituting Known values,we get

$\frac{700 \times 600}{300} = \frac{500 \times \: V _{2} }{293} \\ = = > V_{2} = \frac{14 \times 293}{5} = 820.4ml$

Therefore,the unknown volume is 820.4ml

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