Question

The partial pressure of \[{N_2}\], \[{O_2}\]and \[C{O_2}\]in a vessel are 38cm of Hg, 190 torr and 0.5 atm, respectively.
The total pressure of the mixture at the same temperature is?
A.0.96 atm
B.1.02 atm
C.1.64 atm
D.1.25 atm

Answer 1

Hint: We are provided pressure of all the three molecules in different pressure units. To get the total pressure of the mixture at the same temperature, we need to convert those units into one same unit and add them.
Formula used:
\[{P_{total}} = {P_{{N_2}}} + {P_{{O_2}}} + {P_{C{O_2}}}\]

Complete step by step answer:
There are different units of pressure used.Pressure is defined as force per unit area which is perpendicular to the surface. SI unit of pressure is Pascal or newton per square meter. Bar is also used but it is based on a metric system. For liquids, it is expressed as mmHg and torr for absolute pressure which is 1/760 of standard atmosphere. 1 atm is the standard atmospheric unit of pressure.
 Pressure of nitrogen is 38cm of Hg. We know that \[1cm{\text{ }}Hg{\text{ }} = {\text{ }}10{\text{ }}mm{\text{ }}Hg\], therefore 38cm Hg will be equal to 380 mm Hg.
 \[{P_{{N_2}}} = 380mm\,\,Hg \times \dfrac{{1atm}}{{760mm\,Hg}} = 0.5\,atm\]
 Pressure of oxygen molecules is 190 torr.
 \[{P_{{O_2}}} = 190\,torr \times \dfrac{{1\,atm}}{{760mm\,Hg}} = 0.25\,atm\]
 Pressure of carbon dioxide is already mentioned in atmospheric pressure i.e. 0.5 atm.
 Now, using the formula of total pressure-
 \[{P_{total}} = {P_{{N_2}}} + {P_{{O_2}}} + {P_{C{O_2}}}\]
 Putting the values of each in it, we get the total pressure.
 \[{P_{total}} = 0.5 + 0.25 + 0.5\]
 \[{P_{total}} = 1.25\,atm\]

Hence, the correct option is (D).

Note:
The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases present in a mixture. This is called Dalton’s law or law of partial pressures. It can also be applied to the number of moles.