Question

What is the density of \[C{{O}_{2}}\] at \[{{27}^{o}}C\] and 2.5 atm pressure?

Answer 1

Hint: Carbon dioxide is a gas. Gas laws are used to understand the behaviour of gases. Combining all the gas laws an equation is formulated, using which we can calculate the conditions and how the gas behaves in such conditions. The gas equation is PV=nRT, where P is the pressure, v is the volume, R is the universal gas constant, T is the temperature and n is the number of moles of the gas.

Complete step by step answer:
We know the ideal gas equation is \[PV=nRT\]
It can be also written as \[PM=dRT\]
Where, P is the pressure, M is the molar mass, d is the density, R is the universal gas constant and T is the temperature.

Here T=\[{{27}^{o}}C\] =27+273=300K
Molar mass of carbon dioxide = 44g/mol
P=2.5 atm
Therefore, substituting the values we get
\[2.5\times 44=d\times 0.0821\times 300\]
\[d=\dfrac{2.5\times 44}{0.082\times 300}=4.46g{{L}^{-1}}\]
Thus, the density of \[C{{O}_{2}}\] at \[{{27}^{o}}C\] and 2.5 atm pressure is \[4.46g{{L}^{-1}}\].

Additional Information:
-Ideal gas law describes the behaviour of an ideal gas. Actually ideal gas is a hypothetical gas whose behaviour can be explained by the ideal gas law and the kinetic molecular theory of gases. We know that standard temperature and pressure (STP) is at 298K and 1atm and standard volume is 1 mol of an ideal gas at STP is 22.4L. All empirical gas relationships are special cases of the ideal gas in which any two of the parameters, out of the four, is held constant. Ideal gas laws give values of the fourth quantity of the gas, by keeping any two parameters constant. It is also used to find the density of a gas if its molar mass is known and vice versa.

Note: Universal gas constant has other values based on its unit. When volume is involved we use the value $R = 0.0821Latm/mol$ , the same is used above. When energy is involved we use R = 8.314 $J/kmol$ or in calories its value is R = 1.986$C/Kmol$.