To calculate the volume of the gas, we can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, let's convert the given temperature from degrees Celsius to Kelvin by adding 273.15:
T = 27°C + 273.15 = 300.15 K
Next, we need to find the number of moles of carbon dioxide. We can use the molar mass of carbon dioxide to convert the mass to moles.
The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.
Number of moles = mass / molar mass
Number of moles = 5.5 kg / (44.01 g/mol)
Number of moles ≈ 124.89 mol
Now we can plug all the values into the ideal gas law equation to solve for the volume:
PV = nRT
V = (nRT) / P
V = (124.89 mol * 8.314 J/(mol·K) * 300.15 K) / 101,300 Pa
Converting Pascal (Pa) to kilopascal (kPa):
V = (124.89 mol * 8.314 J/(mol·K) * 300.15 K) / 101.3 kPa
Simplifying the calculation:
V ≈ 2959 m³
Rounding the answer to the nearest whole number:
V ≈ 2959 m³
Therefore, the volume of the gas in a fire extinguisher at a temperature of 27°C and a pressure of 101.3 kPa is approximately 2959 m³.
(let me know if this helps!^^)