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Answer :
The final volume can be determined using Charles's law. The volume of gas at -39.9 degree Celsius will be 6.7 dm³.
What is Charles's law of gases ?
According to Charles's law, at constant pressure, the volume of a gas is directly proportional to the temperature.
Hence, V/T = constant.
Let, V1 and T1 be the initial volume and temperature and V2, T2 be the final quantities.
then, V1/T1 = V2/T2.
V2 = V1 T2/ T1
Given, V1 = 8.9 dm³
T1 = 38.8 °C = 311.8 K
T2 = -39.9 °C = 233.1 K
Then, V2 = 8.9 dm³ × 233.1 K /311.8 K = 6.7 dm³
Therefore, the volume of the gas reduces to 6.7 dm³
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Final answer:
Using Charles's Law, the volume of hydrogen gas at -39.9 degrees Celsius with pressure held constant is calculated to be 6.75 dm³ from the original volume of 8.97 dm³ at 38.8 degrees Celsius.
Explanation:
To find the volume of hydrogen gas at -39.9 degrees Celsius when it originally occupies 8.97 dm³ at 38.8 degrees Celsius with constant pressure, we use Charles's Law. Charles's Law states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to the absolute temperature (V/T = k). Therefore, we can express this as V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
To apply Charles's Law, we need to convert the temperatures from Celsius to Kelvin by adding 273.15 degrees. This gives us T1 = 38.8 + 273.15 = 311.95 K and T2 = -39.9 + 273.15 = 233.25 K. Plugging these values into the formula gives us:
8.97 dm³ / 311.95 K = V2 / 233.25 K
Solving for V2 (the final volume) yields:
V2 = (8.97 dm³ / 311.95 K) * 233.25 K
V2 = 8.97 dm³ * (233.25 K / 311.95 K)
V2 = 6.75 dm³
The volume of hydrogen gas at -39.9 degrees Celsius, with pressure held constant, will be 6.75 dm³.
