Final answer:
Using Charles's Law to find the new volume after a temperature change, the volume of hydrogen gas changes from 5.00 dm³ at 127°C to 2.50 dm³ at -73°C, with pressure held constant. The closest correct option is A.
Step-by-step explanation:
The student asked what the new volume would be if the temperature of a certain mass of hydrogen, initially at 127°C and occupying 5.00 dm³, is changed to -73°C while keeping pressure constant. To solve this, we use Charles's Law which is expressed 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. Remember to convert temperatures to Kelvin by adding 273.15 to the Celsius temperatures.
For the initial state, T1 is 127°C + 273.15 = 400.15 K. The final temperature T2 is -73°C + 273.15 = 200.15 K. Plugging in the values into Charles's Law formula gives:
5.00 dm³ / 400.15 K = V2 / 200.15 K
When we solve for V2, we get:
V2 = (5.00 dm³ × 200.15 K) / 400.15 K
V2 = 2.50 dm³
Thus, the new volume of the hydrogen gas at -73°C would be 2.50 dm³. Hence, option A is closest and correct.