What pressure in kpa is exerted by 94.6 g CO2 at 57°C in 0.750 dm 3
To calculate the pressure exerted by a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in kPa)
V = volume (in dm^3)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values to the appropriate units:
- Mass of CO2 = 94.6 g
- Volume = 0.750 dm^3
- Temperature = 57°C
1. Convert mass to moles:
- To convert the mass of CO2 to moles, we need to know its molar mass.
- The molar mass of CO2 = 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol
- Moles of CO2 = mass of CO2 / molar mass of CO2
moles of CO2 = 94.6 g CO2 / 44.01 g/mol CO2
2. Convert temperature to Kelvin:
- Kelvin = Celsius + 273.15
Temperature in Kelvin = 57°C + 273.15
Now that we have the number of moles and temperature in Kelvin, we can substitute these values into the ideal gas law equation to solve for pressure (P):
PV = nRT
P * 0.750 dm^3 = (94.6 g CO2 / 44.01 g/mol CO2) * (8.314 J/(mol·K)) * (57°C + 273.15)
Now, let's solve for P:
P = ((94.6 g CO2 / 44.01 g/mol CO2) * (8.314 J/(mol·K)) * (57°C + 273.15)) / 0.750 dm^3
Calculate the numerator of the equation separately:
Numerator = (94.6 g CO2 / 44.01 g/mol CO2) * (8.314 J/(mol·K)) * (57°C + 273.15)
Finally, divide the numerator by 0.750 dm^3 to find the pressure (P):
P = Numerator / 0.750 dm^3
After performing the calculations, you will obtain the pressure exerted by 94.6 g of CO2 at 57°C in 0.750 dm^3.