Question

if 5.0 moles of o^(2) and 3.0 moles of N_(2 )are placedin a 30.0 l take at a temperature of 25^(0 )c, what will the pressure of the resulting maxture of gases be?

Answer 1

Explanation:

In order to find the pressure of the mixture, you need to know the total number of moles present in the mixture.

The problem provides you with the volume of the container and the temperature at which the gases are kept, which means that you can use the total number of moles in the ideal gas law to find the *pressure8 of the mixture.

So, the total number of moles present in the container will be

ntotal = nO2 + nN2

ntotal = 5.0 moles + 3.0 moles

=8.0 moles

Now, the ideal gas law equation looks like this

PV = nRT ,where

P - the total pressure of the mixture

V - the volume it occupies

n - the total number of moles of gas in the mixture

R - the universal gas constant, usually given as

0.0821 = atm.L / mol.K

T - the absolute temperature of the gas

Rearrange to solve for P and plug in your values to find

PV = nRT

⇒P=nRT / V

8.0 moles⋅0.0821 atm⋅L / mol⋅K

⋅

absolute temperature

P = .(273.15 + 25) K / 30.0 L

P = 6.5 atm →

rounded to two sig figs

ALTERNATIVE APPROACH

You can check the result by using Raoult's Law, which tells you that the total pressure of a gaseous mixture will be equal to the sum of the partial pressures of each component of that mixture.

Pmix = PO2 + PN2

To get the partial pressures of the two gases, assume that each gas occupies the given volume alone.

For oxygen gas, you will have

5.0moles⋅0.0821 atm⋅L / mol⋅K

PO2 = .(273.15 + 25 K) / 30.0L

PO2 = 4.08 atm

For nitrogen gas, you will have

PN2

3.0moles . 0.0821 atm⋅L / mol⋅K

PN2 = .(273.15 + 25 K) / 30.0L

PN2 = 2.45 atm

The total pressure of the mixture will once again be

Pmix = 4.08 atm + 2.45 atm

= 6.5 atm

rounded to two sig figs

❤Sweetheart❤