Calculating the Gas

To determine whether the gas is NO or N2O, we need to use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. At STP, the pressure is 1 atm and the temperature is 273 K.

Calculating the Number of Moles

We can use the given mass of the gas and its molar mass to calculate the number of moles. The molar mass of NO is 30 g/mol, while the molar mass of N2O is 44 g/mol.

For NO:
n = m/M = 7.5 g / 30 g/mol = 0.25 mol

For N2O:
n = m/M = 7.5 g / 44 g/mol = 0.17 mol

Calculating the Volume

Now that we know the number of moles, we can use the ideal gas law to calculate the volume of the gas.

For NO:
PV = nRT
V = nRT/P = (0.25 mol)(0.0821 L·atm/mol·K)(273 K)/(1 atm) = 5.6 L

For N2O:
PV = nRT
V = nRT/P = (0.17 mol)(0.0821 L·atm/mol·K)(273 K)/(1 atm) = 3.8 L

Conclusion

Since the volume calculated for NO is 5.6 L, which matches the given volume, we can conclude that the gas is NO.