Question

A sample of helium has a temperature of 450 K. The gas is cooled to 248.9 K at which time the gas occupies 103.4 L? Assume pressure is constant at 3 atm. What was the original volume of the gas

Answer 1

Answer:

$\boxed{\text{163.3 L}}$

Explanation:

The pressure is constant, so, to calculate the volume, we can use Charles' Law:

\dfrac{V_{1}}{T_{1}} = \dfrac{V_{2}}{T_{2}}

Data:

V₁ = ?;            T₁ =    450 K

V₂ = 103.4 L; T₂ = 284.9 K

Calculation:

$\dfrac{ V_{1}}{450} = \dfrac{ 103.4}{284.9}\\\\{ V_{1}} = 450 \times \dfrac{103.4}{284.9}\\\\ = \textbf{163.3 L}\\\text{The original volume of the helium was \boxed{\textbf{163.3 L}} }$

Answer 2

The original volume of the gas is 186.94 Liters

Further Explanation;

Charles' Law

• Charles's law states that the volume of a fixed mass of a gas is directly proportional to absolute temperature at constant pressure.

That is;$V\alpha T$

$P=kT$,  where k is a constant

At different temperatures and pressure then;

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

In the Question;

We are given

$V_{1} = ?\\T_{1} = 450\\V_{2} = 103.4 l\\T_{2} =248.9K$

Therefore;

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

$V_{1} =\frac{(103.4 L)(450 K)}{(248.9K)}$

$V_{1} = 186.94Liters$

Other Gas laws

Boyle's law

• Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to its pressure at a constant temperature.

That is;

$P\alpha \frac{1}{V}$

$P\alpha \frac{k}{V}$, where k is a constant

Combined gas law

• Combined gas law combines both Boyle's law and Charles's law.
• It states that the volume of a fixed mass of a gas is directly proportional to absolute temperature and inversely proportional to pressure.
• That is;

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

Pressure Law

• Pressure Law states that the pressure occupied by a gas is directly proportional to absolute temperature.

Keywords: Combined gas laws, Boyle's law and Charles's law

Learn more about:

• Boyles’s law: brainly.com/question/1158880
• Gay-Lussac’s law: brainly.com/question/2438000
• Charles’s law:brainly.com/question/2438000
• Combined gas law: brainly.com/question/2441061

Level: High school

Subject: Chemistry

Topic: Gas laws

Sub-topic: Charles's law