What pressure will be exerted by 10 moles of hydrogen gas in a 7.5 L cylinder at 20°C? (Given: R = 8.314 L∙kPa/K∙mol)
Use the ideal gas law:
P V = n R T,
which tells you that
P = n R T/V
n = 10.0 moles
T = 293 K
V = 7.5 L
Solve for P in Pascals
To find the pressure exerted by the hydrogen gas, we can use the ideal gas law:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in L)
n = Number of moles
R = Ideal gas constant (8.314 L∙kPa/K∙mol)
T = Temperature (in K)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20°C + 273.15
T(K) = 293.15 K
Now we can plug in the values into the ideal gas law equation:
P * 7.5 = 10 * 8.314 * 293.15
Rearranging the equation to solve for P:
P = (10 * 8.314 * 293.15) / 7.5
Calculating:
P = 3116.49 kPa
Therefore, the pressure exerted by 10 moles of hydrogen gas in a 7.5 L cylinder at 20°C is approximately 3116.49 kPa.
To find the pressure exerted by a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in kPa)
V is the volume (in liters)
n is the number of moles of gas
R is the ideal gas constant (8.314 L∙kPa/K∙mol)
T is the temperature (in Kelvin)
To solve the problem, we need to convert the given temperature from °C to Kelvin. The Kelvin scale is obtained by adding 273.15 to the Celsius temperature, so T = 20°C + 273.15 = 293.15 K.
Now, we can substitute the known values into the ideal gas law equation:
P * 7.5 L = 10 mol * (8.314 L∙kPa/K∙mol) * 293.15 K
Simplifying the equation by multiplying the values together:
P * 7.5 L = 2470.209 L∙kPa
To solve for P, divide both sides of the equation by 7.5 L:
P = 2470.209 L∙kPa / 7.5 L
P ≈ 329.4 kPa
Therefore, the pressure exerted by 10 moles of hydrogen gas in a 7.5 L cylinder at 20°C is approximately 329.4 kPa.