Final answer:
The pressure exerted by 0.275 moles of N₂ gas in a 0.5 dm³ flask at 273 K can be calculated using the Virial equation, considering the given B value and the gas constant in suitable units. Final calculations will give the pressure in kPa.
Step-by-step explanation:
To calculate the pressure exerted by 0.275 moles of N₂ gas in a 0.5 dm³ flask at 273 K using the first two terms of the series in the Virial equation and given that the value of B for N₂ gas at 273 K is -10.5 cm³/mole, we need to use the equation:
PV = nRT + (n^2)B / V
By rearranging for pressure (P) and substituting the given values, we can solve for P. We must convert the volume of the flask from dm³ to cm³ to be consistent with the units of B. The volume in cm³ is 500 cm³ (since 1 dm³ = 1000 cm³).
P = (nRT/V) + (n^2)B / V²
P = (0.275 moles * 8.3145 J/K mol * 273 K / 500 cm³) + ((0.275 moles)² * -10.5 cm³/mole) / (500 cm³)²
Converting Joules to kPa by dividing by 10³ and cm³ to m³ by multiplying by 10⁻⁶, we get the final pressure in kPa.
After performing the calculations, substitute the numerical results into the expression to obtain the pressure in kPa.
The unit of pressure in these calculations will be in kPa, where 1 Pa = 1 kg/(m.s²).