Question 5.7: Density Calculate the density of nitrogen gas at 125 °C and ...
Density
Calculate the density of nitrogen gas at 125 °C and a pressure of 755 mmHg.
| SORT The problem gives you the temperature and pressure of a gas and asks you to find its density. The problem states that the gas is nitrogen. | GIVEN T = (°C) = 125 °C, P = 755 mmHg FIND d |
| STRATEGIZE Equation 5.6 provides the relationship between the density of a gas and its temperature, pressure, and molar mass. The temperature and pressure are given, and you can calculate the molar mass from the formula of the gas, which you know is N2. | CONCEPTUAL PLAN
P,T,M → d . d=\frac{PM}{RT} RELATIONSHIPS USED d=\frac{PM}{RT} (density of a gas) |
| SOLVE To solve the problem, you must gather each of the required quantities in the correct units. Convert the tempera ture to kelvins and the pressure to atmospheres. Substitute the quantities into the equation to calculate density. |
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T(K) = 125 + 273 = 398 K
P = 755 \cancel{mmHg} \times\frac{1 atm}{760 \cancel{mmHg}} = 0.99\underline{3}42 atm
d =\frac{ PM}{RT}
=\frac{(0.99\underline{3}42 \cancel{atm}) (28.02 \frac{g}{\cancel{mol}} )}{(0.08206 \frac{L . \cancel{atm}}{\cancel{mol} . \cancel{K}}) (398 \cancel{K})}
= 0.852 g/L
CHECK The units of the answer are correct. The magnitude of the answer (0.852 g/L) makes sense because earlier we calculated the density of nitrogen gas at STP as 1.25 g/L. Since the temperature is higher than standard temperature and pressure, the density should be lower.