Final answer:
The gauge pressure of a gas cylinder cannot be accurately calculated without additional data or the specific compressibility chart for the gas mixture.
Step-by-step explanation:
The question asks for the gauge pressure of a gas cylinder filled with a mixture of N₂O and N₂ at a temperature of 24.0 °C. To find the gauge pressure, we would need to calculate the total number of moles of each gas in the mixture, apply the ideal gas law (PV = nRT), and adjust for the compressibility factor if necessary. However, since no specific volume or compressibility chart is provided within the question and the provided reference information is not directly applicable, a precise calculation cannot be done without additional data. Therefore, it's advisable to check if there's further information or context available to accurately calculate the gauge pressure.