Question

the total pressure of a mixture of three gases is 2.8 atm. gas 1 has a partial pressure of 480 mm Hg,gas 2 has a partial pressure of 1450 torr, and the partial pressure of gas 3 is unkown. what is the partial pressure of gas 3 in atm

Answer 1

Hence, the partial pressure of gas 3 in atm = 0.3 atm

Step-by-step explanation

Given:

Total pressure of the three gases, P(total) = 2.8 atm

Partial pressure of gas 1, P₁ = 480 mmHg

Partial pressure of gas 2, P₂ = 1450 torr

What to find:

The partial pressure of gas 3 in atm.

Step-by-step solution:

According to Dalton's law of partial pressure which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture. i.e

`P_(total)=P_1+P_2+P_3+....P_n`

Since the unit of the given partial pressures are not the same with the that of the total pressure, then you need to convert them to atm.

Conversion factor:

760 mmHg = 1 atm

760 torr = 1 atm

Therefore,

The partial pressure of gas 1, P₁ = 480 mmHg = (480 mmHg/760 mmHg) x 1 atm = 0.6 atm

The partial pressure of gas 2, P₂ = 1450 torr = (1450 torr/760 torr) x 1 atm = 1.9 atm

Putting P₁ = 0.6 atm, P₂ = 1.9 atm and P(total) = 2.8 atm into the partial pressure formula above to get the partial pressure of gas 3:

`\begin{gathered} 2.8atm=0.6atm+1.9atm+P_3 \\ \\ 2.8atm=2.5atm+P_3 \\ \\ P_3=2.8atm-2.5atm \\ \\ P_3=0.3atm \end{gathered}`

Hence, the partial pressure of gas 3 in atm = 0.3 atm