Question

a sample of oxygen gas weighting 8.5g at a pressure of 90.0cm of mercury occupies a volume of 10.5 litre when it temperature is 270 kelvin what is volume when the temperature is raised to 360 kelvin at a same pressure

Answer 1

Answer:

Volume = 14.02 L

Explanation:

Given:

• Weight of oxygen gas = 8.5 g
• Pressure (P₁) = 90 cm of Hg
• Volume (V₁) = 10.5 L
• Temperature = (T₁) = 270 K
• Pressure (P₂) = P₁ = 90 cm of Hg
• Temperature (T₂) = 360 K

To Find:

• Volume (V₂)

Solution:

First convert the pressure from cm of Hg to atm

Hence,

90 cm of Hg = 1.18 atm

Now by ideal gas equation we know that,

$\sf{\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}}$

Substitute the given datas,

$\sf{\dfrac{1.18\times 10.5}{270} =\dfrac{1.18\times V_2}{360} }$

Simplifying the above equation,

$\sf{\dfrac{12.39}{270}=3.28\times 10^{-3} \:V_2}$

3.28 × 10⁻³ V₂ = 0.046

V₂ = 0.046/3.28 × 10⁻³

V₂ = 14.02 L

Hence the gas would occupy a volume of 14.02 L

Notes:

By Charle's law if the pressure is kept constant, volume is directly proportional to temperature.

V ∝ T

By Boyle's law if the temperature is kept constant, pressure is inversely proportional to volume of the gas.

P ∝ 1/V

By Gaylussac's law, if the volume is kept constant, pressure is directly proportional to the temperature.

P ∝ T

Answer 2

Volume = 14.02 L

Explanation:

Given:

Weight of oxygen gas = 8.5 g

Pressure (P₁) = 90 cm of Hg

Volume (V₁) = 10.5 L

Temperature = (T₁) = 270 K

Pressure (P₂) = P₁ = 90 cm of Hg

Temperature (T₂) = 360 K

To Find:

Volume (V₂)

Solution:

First convert the pressure from cm of Hg to atm

Hence,

90 cm of Hg = 1.18 atm

Now by ideal gas equation we know that,

\sf{\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}}

T

1

P

1

V

1

=

T

2

P

2

V

2

Substitute the given datas,

\sf{\dfrac{1.18\times 10.5}{270} =\dfrac{1.18\times V_2}{360} }

270

1.18×10.5

=

360

1.18×V

2

Simplifying the above equation,

\sf{\dfrac{12.39}{270}=3.28\times 10^{-3} \:V_2}

270

12.39

=3.28×10

−3

V

2

3.28 × 10⁻³ V₂ = 0.046

V₂ = 0.046/3.28 × 10⁻³

V₂ = 14.02 L

Hence the gas would occupy a volume of 14.02 L

Notes:

By Charle's law if the pressure is kept constant, volume is directly proportional to temperature.

V ∝ T

By Boyle's law if the temperature is kept constant, pressure is inversely proportional to volume of the gas.

P ∝ 1/V

By Gaylussac's law, if the volume is kept constant, pressure is directly proportional to the temperature.

P ∝ T