Final answer:
Using the combined gas law, the final volume of the gas under the new conditions is approximately 4.58 L. This is calculated by converting temperatures to Kelvin and applying the formula V2 = P1 * V1 * T2 / (P2 * T1) with the given values.
Step-by-step explanation:
Calculating Change in Gas Volume
The question asks to determine the new volume of a gas when its temperature and pressure change. The initial conditions are a volume of 3.35 liters, temperature of 15.00 °C, and pressure of 130 atm. We are asked to find the volume at a new temperature of 18.60 °C and a pressure of 0.966 atm.
To solve this, we can use the combined gas law which relates the initial and final states of a gas when it undergoes changes in pressure (P), volume (V), and temperature (T). The combined gas law equation is:
P1 * V1/T1 = P2 * V2/T2
We need to use the absolute temperatures in Kelvin, so we will convert the Celsius temperatures by adding 273.15:
- T1 = 15.00 + 273.15 = 288.15 K
- T2 = 18.60 + 273.15 = 291.75 K
Now, we can rearrange the combined gas law to solve for the final volume (V2):
V2 = P1 * V1 * T2 / (P2 * T1)
Substituting in the values we have:
V2 = (130 atm * 3.35 L * 291.75 K) / (0.966 atm * 288.15 K)
= 1276.05 L • K / 278.42 atm • K
Final volume (V2) is therefore approximately 4.58 L.