Partial Pressure - Dalton’s Law, Application, Formula, Units, FAQs

Dalton’s Law of Partial Pressure Applicability-

Dalton set a restriction for gases obeying Dalton’s law of partial pressure.

• Gases of the mixture should not react with each other. Some gases like ammonia (NH₃ and HCl) react with each other to form products like ammonium chloride (NH₃Cl). Therefore, Dalton's law of partial pressure does not apply to such gases.

• Similarly, gases like Hydrogen(H₂) and chlorine (Cl₂) react to form hydrogen chloride (HCl).

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Partial Pressure Formula

Let there be a container with gas A and gas B inside it. Gas A and Gas B will have partial pressure pa and pb.

According to the ideal gas equation-

$\begin{aligned} & \mathrm{p}_{\mathrm{a}}=\mathrm{n}_1 \mathrm{RT} / \mathrm{V} \\ & \text { And } p_b=n_2 R T / V\end{aligned}$

Here, n₁ and n₂ are the numbers of moles of gases present in the container.

the total pressure of a mixture of two gases is given by-

$\begin{gathered}\mathrm{P}_{\text {total }}=\mathrm{P}_1+\mathrm{P}_2 \\ =\mathrm{n}_1 \mathrm{RT} / \mathrm{V}+\mathrm{n}_2 \mathrm{RT} / \mathrm{V} \\ =\left(\mathrm{n}_1+\mathrm{n}_2\right) \mathrm{RT} / \mathrm{V}\end{gathered}$

Dividing p₁ by p_total -

$\begin{aligned} & \mathrm{p}_1 / \mathrm{p}_{\text {total }}=\left(\mathrm{n}_1 / \mathrm{n}_1+\mathrm{n}_2\right) \mathrm{RTV} / \mathrm{RTV} \\ & \mathrm{n}_1 / \mathrm{n}_1+\mathrm{n}_2=\mathrm{n}_1 / \mathrm{n}_2=\mathrm{x}_1\end{aligned}$

Where X₁ is the mole fraction of the first Gas.

$p_1=X_1 p_{\text {total }}$

For both gases A and B,

The general equation can be written as-

$p_n=X_n p_{\text {total }}$

This is the formula of partial pressure of any gas.

Where p_n is the partial pressure of nth gas and x_n is the partial pressure of n^th gas.

Also Read:

• NCERT solutions for Class 12 Chemistry Chapter 2 Solutions
• NCERT Exemplar Class 12 Chemistry Solutions Chapter 2 Solutions
• NCERT notes Class 12 Chemistry Chapter 2 Solutions

Units of Partial Pressure-

Partial pressure units are the same as the units of normal pressure.

• The barometer is the instrument used in the lab to measure the pressure. The height of mercury determines the atmospheric units.

• The barometer is assembled using a glass tube. This glass tube is closed from one end and open from the other end. Glass tube is filled with pure mercury. Glass tube is inverted into an open vessel containing mercury. The level of mercury drops until the atmospheric pressure acting outside the glass tube becomes equal to the pressure inside the tube.

• If the height of the column decreases then atmospheric pressure increases and if the height of the column increases then the atmospheric pressure decreases.

It is the maximum height of mercury that determines the pressure. The height keeps falling and raising due to the changes from time to time.

Consider mercury-filled in an inverted glass tube of h cm and area of cross-section be equal to a cm²

We know that

pressure=force/area
Force $=$ mass $\times$ acceleration
pressure=mass $\times$ acceleration/area

$
\begin{aligned}
& \mathrm{P}=\mathrm{mg} / \mathrm{A} \\
& P=d \times V \times g / A
\end{aligned}
$
$
\begin{gathered}
\mathrm{P}=\mathrm{d} \times \mathrm{A} \times \mathrm{h} \times \mathrm{g} / \mathrm{A} \\
=\mathrm{hdg}
\end{gathered}
$

where d is the density, h is the height, g is the gravity, and A is the area.

1 atm is the pressure that supports a mercury height of 76 cm at 0°C

Recommended topic video on (Partial Pressure)

Some Solved Examples

Example 1.Equal weighs of ethane and hydrogen are mixed in an empty container at 25∘C The fraction of the total pressure exerted by Hydrogen is -

Options

a) 1:2

b) 1:1

c) 1:16

d) 15:16

Answer 1

let Xg of each gas is mixed.

$
\begin{gathered}
\text { mole of ethane }=\frac{x}{30} \\
\text { mole of hydrogen }=\frac{x}{2}
\end{gathered}
$
$
\begin{aligned}
\therefore \text { Mole fraction of hydrogen } & =\frac{x / 2}{x / 2+x / 30}=\frac{15}{16} \\
\Rightarrow \frac{\text { partial pressure of } H_2}{\text { Total pressure }} & =\text { mole fraction of Hydrogen } \\
= & 15: 16
\end{aligned}
$

Example 2.

At definite temperature, the tootal pressure of a gas mixture consisting of three gases A,B and C are 2,4,and 6 , then the increasingorder of their partial pressure is ___

a) $P_A=P_B=P_C$
b) P $_{\text {A }}>$ P $_{\mathrm{B}}>$ P $_{\mathrm{C}}$
c) P $_{\mathrm{A}}<$ P $_{\mathrm{B}}<$ P $_{\mathrm{C}}$
d) $P_A \neq P_B \neq P_C$

Answers (a)

The mole fractions of $A, B$, and $C$ in the mixture,

$
\begin{aligned}
& x_A=\frac{2}{12}=\frac{1}{6} \\
& x_B=\frac{4}{12}=\frac{1}{3} \\
& x_C=\frac{6}{12}=\frac{1}{2}
\end{aligned}
$
Therefore, the partial pressure of gas A,

$
\begin{aligned}
\underline{P_A} & =\frac{P}{6} \\
P_B & =\frac{P}{3} \\
\hline P_c & =\frac{P}{2} \\
\therefore \mathrm{P}_{\mathrm{A}}<\mathrm{P}_{\mathrm{B}}<\mathrm{C} &
\end{aligned}
$

Practice more questions from the link given below

For more questions to practice, the following MCQs will help in the preparation for competitive examinations

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