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8.98 dm\(^3\) of hydrogen gas is collected at 38.8 °C. Find the volume the gas will occupy at -39.9 °C if the pressure remains constant.

Answer :

Answer:

6.71dm³

Explanation:

Given parameters:

Initial Volume of hydrogen gas = 8.98dm³

Initial Temperature = 38.8°C; in Kelvin = 38.8 + 273 = 311.8K

Final temperature = -39.9°C; in Kelvin = -39.9 + 273 = 233.1K

Unknown:

Final volume = ?

Solution:

To solve this problem, we apply the Charles's law. It states at;

"The volume of a fixed mass (mole) of a gas varies directly as its absolute temperature if the pressure is constant".

Mathematically;

[tex]\frac{V_{1} }{T_{1} }[/tex] = [tex]\frac{V_{2} }{T_{2} }[/tex]

V and T are temperature values

1 and 2 are the initial and final states

Insert the parameters and solve for V₂

[tex]\frac{8.98}{311.8 }[/tex] = [tex]\frac{V_{2} }{233.1}[/tex]

V₂ x 311.8 = 8.98 x 233.1

V₂ = 6.71dm³

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