A dentist has a 5.00 L cylinder of N2O at 20.0 atm and 25 degrees C what is the mass of gas in the cylinder
To calculate the mass of gas in the cylinder, you need to use the ideal gas law equation, which relates the pressure, volume, temperature, and number of moles of a gas.
1. Convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25°C + 273.15 = 298.15 K
2. Convert the given pressure from atm to Pascal (Pa):
P(Pa) = P(atm) × 101325
P(Pa) = 20.0 atm × 101325 = 2026500 Pa
3. Solve for the number of moles of N2O using the ideal gas law equation:
PV = nRT
n = PV / RT
Where:
P = pressure (Pa)
V = volume (L)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (K)
n = (2026500 Pa × 5.00 L) / (0.0821 L·atm/(mol·K) × 298.15 K)
4. Calculate the molar mass of N2O, which is the sum of the atomic masses of nitrogen (N) and oxygen (O):
Molar mass of N2O = (2 × atomic mass of N) + atomic mass of O
Atomic mass of N = 14.01 g/mol
Atomic mass of O = 16.00 g/mol
Molar mass of N2O = (2 × 14.01 g/mol) + 16.00 g/mol = 44.02 g/mol
5. Finally, calculate the mass of the gas in the cylinder using the number of moles obtained in step 3 and the molar mass of N2O obtained in step 4:
Mass of gas = number of moles × molar mass
Substitute the values into the equation and calculate:
Mass of gas = n × Molar mass of N2O
Now you have all the information needed to calculate the mass of gas in the cylinder.
Use PV = nRT and solve for n.
Then n = grams/molar mass, solve for grams.