a sample of xenon gas occupies a volume of 6.56 l6.56 l at 499 k.499 k. if the pressure remains constant, at what temperature will this same xenon gas sample have a volume of 3.38 l?

Charles' law, which states that, provided the pressure is constant, the volume occupied by a particular quantity of gas is directly proportional to the absolute temperature. According to the law, volume increases with increasing temperature and decreases with decreasing temperature, applies when pressure is constant. The relationship equation for the Charles's law can be written as-

[tex]V_{i}[/tex]/[tex]T_{i}[/tex]= [tex]V_{f}[/tex]/[tex]T_{f}[/tex]

where,

[tex]V_{i}[/tex] = initial volume

[tex]T_{i}[/tex] = initial absolute temperature

[tex]V_{f}[/tex] = final volume

[tex]T_{f}[/tex] = final absolute temperature

According to the given question,

[tex]V_{i}[/tex] = 6.56 litres, [tex]T_{i}[/tex] = 499 Kelvin, [tex]V_{f}[/tex] = 3.38 litres, [tex]T_{f}[/tex] = ?

The temperature is given in Kelvin so we can put it as it is. So, on applying the given values in the formula:

6.56 / 499 = 3.38 / [tex]T_{f}[/tex]

Now, for final temperature we can rearrange the equation to get-

[tex]T_{f}[/tex] = (3.38 × 499) / 6.56

[tex]T_{f}[/tex] = 257.1 K

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