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 press

Question

Otrada [13]

2 years ago

10

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 press

ure is constant at 3 atm. What was the original volume of the gas

Chemistry

2 answers:

Umnica [9.8K] · Answer 1 · 2023-08-28T11:57:45+03:00

Umnica [9.8K]2 years ago

5 0

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 $\boxed{\textbf{163.3 L}}$}$

IRINA_888 [86] · Answer 2 · 2023-08-28T13:48:57+03:00

The original volume of the gas is 186.94 Liters

Further Explanation;

<h3>Charles' Law </h3>

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;

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

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

$V_{1} = 186.94Liters$

<h3>Other Gas laws </h3><h3>Boyle's law </h3>

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

<h3>Combined gas law</h3>

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;

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