Question

Suppose that Daniel has a 2.50 L bottle that contains a mixture of O₂, N₂, and CO₂ under a total pressure of 5.40 atm. He knows that the mixture contains 0.310 mol N₂ and that the partial pressure of CO₂ is 0.250 atm. If the temperature is 273 K. what is the partial pressure of O₂?

Answer 1

To find the partial pressure of O2, we use Dalton's law of partial pressures along with the ideal gas law. We first calculate the partial pressure of N2, then subtract this value, along with the partial pressure of CO2, from the total pressure to get the partial pressure of O2, which is 2.43 atm.

Step-by-step explanation:

We can use Dalton's law of partial pressures to find the partial pressure of O2. Dalton's law states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas in the mixture. Since the total pressure and the partial pressures of N2 and CO2 are known, we can solve for the partial pressure of O2.

The partial pressure of N2 can be found using the ideal gas law, which is PV=nRT. We have the number of moles of N2 and the temperature, so we can solve for the pressure of N2 (PN2) assuming the volume V is the volume of the bottle.

PN2 = (NRT)/V

Where:

n = moles of N2 = 0.310 mol

R = ideal gas constant = 0.0821 L·atm/(mol·K)

T = temperature = 273 K

V = volume of the bottle = 2.50 L

First, we calculate PN2:

PN2 = (0.310 mol × 0.0821 L·atm/(mol·K) × 273 K) / 2.50 L = 2.72 atm

Since the total pressure is 5.40 atm and the partial pressure of CO2 is 0.250 atm, we can calculate the partial pressure of O2 using Dalton's law:

PO2 = Ptotal - PN2 - PCO2

PO2 = 5.40 atm - 2.72 atm - 0.250 atm = 2.43 atm

Therefore, the partial pressure of O2 in the mixture is 2.43 atm.