A given amount of gas occupies \(10.0\mathrm{dm}^{5}\) at 4atm and 273°C. The number of moles of the gas present is [Molar volume of gas at s.t.p = \(22.4\m...

The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. We can use this equation to solve for the number of moles of gas present. First, we need to convert the volume from dm5 to dm3, which is the same as liters (L). So, 10.0 dm5 is equal to 10.0/1000 = 0.01 dm3 or 0.01 L. Next, we need to convert the temperature from Celsius to Kelvin by adding 273 to get 546 K. Now we can plug in the values we have into the ideal gas law: 4 atm x 0.01 L = n x 0.0821 L·atm/K·mol x 546 K Simplifying, we get: 0.04 = n x 44.8 Solving for n, we get: n = 0.04/44.8 = 0.00089 mol Finally, we can compare this value to the molar volume of a gas at standard temperature and pressure (STP), which is 22.4 L/mol. To do this, we need to convert the volume of gas we have to STP conditions. Since the temperature is already at STP (273 K), we just need to adjust the pressure. Using the ideal gas law, we can solve for the volume at STP: 1 atm x V = 0.00089 mol x 0.0821 L·atm/K·mol x 273 K Simplifying, we get: V = 0.0224 L or 22.4 dm3 Therefore, the amount of gas present is equal to 0.00089 mol, which is less than 1 mol. So the answer is 0.89 mol.