Question

Gas sample has a volume of 0.287 L with an unknown temperature. The same gas has a volume of 0.180 L when the temperature is 37∘C, with no change in the pressure or amount of gas.

What was the initial temperature, in degrees Celsius, of the gas?

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Answer 1

205.3°C

Step-by-step explanation:

Given parameters:

V₁ = 0.287L

V₂ = 0.18L

T₂ = 37°C

Unknown:

T₁ = ?

Solution:

Since we are interested in volume and temperature relationships in a fixed pressure of the balloon, Charles's law will be a perfect solution to this problem.

Charles's law states that "At constant pressure, the volume of a fixed mass of gas is directly proportional to its temperature".

Mathematically;

`(V_(1) )/(T_(1) ) = (V_(2) )/(T_(2) )`

where V and T are volume and temperature of the gas

1 and 2 are initial and final states;

let us convert T₂ = 37°C to K; 37 + 273 = 300K

Input the parameters and solve for the unknown;

`(0.287)/(x) = (0.18)/(300)`

T₁ = 478.3K

Now convert back to °C; 478.3 - 273 = 205.3°C