Calculate the density of ammonia (NH₃) gas in a 4.32 L container at 837 torr and 45 °C.

Question

Quizplus · Accepted Answer

To calculate the density of ammonia gas under the given conditions, we can use the ideal gas law equation rearranged to solve for density ($ \rho $):$$ \rho = \frac{PM}{RT} $$where:- $ P $ is the pressure in atmospheres (atm),- $ M $ is the molar mass of the gas in grams per mole (g/mol),- $ R $ is the ideal gas constant (0.0821 L·atm/(K·mol)),- $ T $ is the temperature in Kelvin (K).First, convert the given pressure from torr to atm:$$ 837 \, \text{torr} \times \frac{1 \, \text{atm}}{760 \, \text{torr}} = 1.101 \, \text{atm} $$Convert the temperature from Celsius to Kelvin:$$ 45 \, ^\circ\text{C} + 273.15 = 318.15 \, \text{K} $$The molar mass of ammonia (NH$_3$) is calculated as follows:- N: 14.01 g/mol- H: 1.008 g/mol $ \times 3 = 3.024 \, \text{g/mol} $- Total: 17.034 g/molNow, plug the values into the density equation:$$ \rho = \frac{(1.101 \, \text{atm}) \times (17.034 \, \text{g/mol})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (318.15 \, \text{K})} $$$$ \rho = \frac{18.739 \, \text{g/mol}}{26.111 \, \text{L·mol/K}} $$$$ \rho = 0.718 \, \text{g/L} $$Therefore, the density of ammonia gas under the given conditions is approximately 0.719 g/L.

Calculate the Density of Ammonia (NH3) Gas in a 4

Calculate the Density of Ammonia (NH₃) Gas in a 4