Final answer:
To calculate the volume of 2.58 moles of a gas at 37.5°C and 95.8 kPa, we use the ideal gas law PV = nRT. After converting temperature to Kelvin and pressure to atm (if necessary), we can solve for volume by rearranging the equation to V = nRT/P.
Step-by-step explanation:
Calculating the Volume of a Gas
The question requires us to calculate the volume of 2.58 moles of gas at a temperature of 37.5°C and a pressure of 95.8 kPa using the ideal gas law, which is expressed as PV = nRT. The ideal gas constant (R) value in kPa can be derived from the given standard conditions where 1 mole of any gas at STP occupies 22.414 L, the standard temperature is 273.15 K, and the standard pressure is 101.325 kPa. By substituting these values into the ideal gas equation, we can solve for R.
To find the volume at the given conditions, firstly, we need to convert the temperature to Kelvin by adding 273.15 to the Celsius temperature. Therefore, T = 37.5 °C + 273.15 = 310.65 K. Now, we can rearrange the ideal gas equation to solve for volume (
V): V =
nRT / P. Plugging in the values (with R in the correct units), we can calculate the volume of the gas under the given conditions.
Remember to convert the pressure to atm if you are using the R-value for L-atm/mol-K which is 0.08206. To convert kPa to atm, we divide the pressure in kPa by 101.325 kPa/atm. Thus, P in atm = 95.8 kPa / 101.325 kPa/atm.