Final answer:
The final pressure of a gas that expands from 1 liter at 10.0 °C to 10 liters at 100.0 °C, starting with an original pressure of 3 atmospheres, is 0.3953 atmospheres.
Step-by-step explanation:
To calculate the final pressure of a gas that expands from 1 liter at 10.0 °C to 10 liters at 100.0 °C with an original pressure of 3 atmospheres, we can use the combined gas law formula: P1/V1/T1 = P2/V2/T2, where P stands for pressure, V stands for volume, and T stands for temperature in Kelvin. First, we need to convert the temperatures to Kelvin by adding 273.15: T1 = 10.0°C + 273.15 = 283.15 K and T2 = 100.0°C + 273.15 = 373.15 K. Now we can insert the values into the combined gas law equation: (3 atm * 1 L)/283.15 K = (P2 * 10 L)/373.15 K. To solve for P2, the unknown final pressure, we rearrange the equation: P2 = (3 atm * 1 L / 10 L) * (373.15 K/283.15 K). After performing the calculations: P2 = (0.3 atm) * (373.15/283.15) = 0.3 atm * 1.3177 = 0.3953 atm. Therefore, the final pressure of the gas is 0.3953 atmospheres.