A gas sample occupies a container of 25.0 mL with a pressure of 125.1 kPa at room temperature (25.0 °C). The number of moles of this gas in the container is
Use V = nRT. Substitute and solve for n.
To find the number of moles of gas in the container, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in Pascals)
V = volume of the gas (in cubic meters)
n = number of moles of the gas
R = ideal gas constant (8.31 J/(mol K))
T = temperature of the gas (in Kelvin)
First, let's convert the given values to the correct units:
- The pressure is given as 125.1 kPa. We need to convert it to Pascals, so we multiply it by 1000 (since 1 kPa = 1000 Pa).
- The volume is given as 25.0 mL. We need to convert it to cubic meters, so we divide it by 1000 (since 1 L = 1000 mL = 0.001 m^3).
- The temperature is given as 25.0 °C. We need to convert it to Kelvin, so we add 273.15 (since K = °C + 273.15).
Now, let's calculate the number of moles (n) using the rearranged ideal gas law equation:
n = PV / RT
n = (P * V) / (R * T)
Substituting the given values into the equation:
n = (125.1 kPa * 25.0 mL / 1000) / (8.31 J/(mol K) * (25.0 °C + 273.15))
n = (125.1 * 10^3 Pa * 25.0 * 10^-6 m^3) / (8.31 J/(mol K) * (25.0 + 273.15) K)
n = (125.1 * 25.0 * 10^-6)/(8.31 * (25.0 + 273.15))
Calculating this expression will give us the number of moles of gas in the container.