To find the pressure of the oxygen gas in the cylinder, you can use the ideal gas law, which relates pressure (P), volume (V), the number of moles (n), and temperature (T) for an ideal gas:
PV = nRT
Where:
P = Pressure (in atmospheres, atm)
V = Volume (in liters, L)
n = Number of moles (in moles, mol)
R = Ideal gas constant (approximately 0.0821 L·atm/mol·K)
T = Temperature (in Kelvin, K)
First, you need to find the number of moles of oxygen gas (O2) using the given mass and the molar mass of O2.
Find the molar mass of O2:
The molar mass of O2 is approximately 32 g/mol (16 g/mol for each oxygen atom).
Calculate the number of moles (n) using the given mass:
n = Mass (in grams) / Molar mass (in g/mol)
n = 51.3 g / 32 g/mol ≈ 1.603 moles
Now that you have the number of moles, you can calculate the pressure using the ideal gas law. However, you need to convert the temperature from Celsius to Kelvin:
T(K) = 23°C + 273.15 ≈ 296.15 K
Now, plug the values into the ideal gas law:
PV = nRT
P(8.58 L) = (1.603 moles)(0.0821 L·atm/mol·K)(296.15 K)
Now, solve for P:
P ≈ (1.603 moles * 0.0821 L·atm/mol·K * 296.15 K) / 8.58 L ≈ 3.036 atm
So, the pressure of the oxygen gas in the cylinder is approximately 3.036 atmospheres (atm) at 23°C.