Air consists of 21 % oxygen, 78 % nitrogen and 1 % argon by volume. Calculate:

* (a)  the partial pressures in Pa, if total pressure is 1 atm, 

* (b)  the concentration in mol m–3, of each gas at 273 K, 

* (c)  the average molar mass of air, 

* (d)  the number of oxygen molecules in 15 g air.

You're posting about 20 or more questions with these 5. We are here to help with the emphasis on help but we expect you to do most of the work.

a. The mole fractions are 0.21 for oxygen; 0.78 for nitrogen and 0.01 for argon. Then pO2 = XO2*Ptotal
pN2 = XN2*Ptotal
pAr =XAr*Ptotal.

Having a should allow you to do b,c,d. Post your work if you get stuck.

To answer these questions, we need to apply the ideal gas law. The ideal gas law equation is given by:

PV = nRT

Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant, and
T is the temperature in Kelvin.

Let's start answering each question.

(a) To find the partial pressures in Pascal (Pa), we need to calculate the partial pressure of each gas, assuming the total pressure is 1 atmosphere (atm).

Given:
Oxygen (O2) = 21% by volume
Nitrogen (N2) = 78% by volume
Argon (Ar) = 1% by volume

We'll convert the percentages to fractions:
Oxygen (O2) = 0.21
Nitrogen (N2) = 0.78
Argon (Ar) = 0.01

Since we have the total pressure as 1 atm, the partial pressure of each gas can be calculated as:

Partial pressure of oxygen (PO2) = 0.21 * 1 atm = 0.21 atm
Partial pressure of nitrogen (PN2) = 0.78 * 1 atm = 0.78 atm
Partial pressure of argon (PAr) = 0.01 * 1 atm = 0.01 atm

To convert the partial pressures from atm to Pascal (Pa), we use the conversion factor:
1 atm = 101325 Pa

Therefore,
Partial pressure of oxygen (PO2) = 0.21 atm * 101325 Pa = 21248.25 Pa
Partial pressure of nitrogen (PN2) = 0.78 atm * 101325 Pa = 79035.5 Pa
Partial pressure of argon (PAr) = 0.01 atm * 101325 Pa = 1013.25 Pa

So, the partial pressures are:
PO2 = 21248.25 Pa
PN2 = 79035.5 Pa
PAr = 1013.25 Pa

(b) To calculate the concentration in mol m–3 of each gas at 273 K, we need to use the ideal gas law equation:

PV = nRT

Rearranging the equation to solve for n (number of moles), we have:

n = PV / RT

Given:
Temperature (T) = 273 K
Partial pressure of oxygen (PO2) = 21248.25 Pa
Partial pressure of nitrogen (PN2) = 79035.5 Pa
Partial pressure of argon (PAr) = 1013.25 Pa
Gas constant (R) = 8.314 J/(mol·K)

For each gas, we can calculate the concentration (n/V) in mol m–3 as:

Concentration of oxygen (CO2) = (PO2) / (RT) = (21248.25 Pa) / (8.314 J/(mol·K) * 273 K)
Concentration of nitrogen (CN2) = (PN2) / (RT) = (79035.5 Pa) / (8.314 J/(mol·K) * 273 K)
Concentration of argon (CAr) = (PAr) / (RT) = (1013.25 Pa) / (8.314 J/(mol·K) * 273 K)

Calculate each concentration individually to get the final answer.

(c) To find the average molar mass of air, we need to consider the molar masses of each gas present in the air mixture and their respective amounts.

Given:
Oxygen (O2) - molar mass (Molecular weight) = 32 g/mol
Nitrogen (N2) - molar mass (Molecular weight) = 28 g/mol
Argon (Ar) - molar mass (Molecular weight) = 40 g/mol

Using the percentage by volume, the weighted average molar mass of air can be calculated as:

Average molar mass of air = (Molar mass of oxygen * volume fraction of oxygen) + (Molar mass of nitrogen * volume fraction of nitrogen) + (Molar mass of argon * volume fraction of argon)

Calculate each part separately and then sum them up to get the final answer.

(d) To find the number of oxygen molecules in 15 g of air, we need to use the concept of moles and Avogadro's number.

Given:
Molar mass of oxygen (O2) = 32 g/mol

First, calculate the number of moles of oxygen in 15 g of air using the molar mass:

Number of moles of oxygen (n) = Mass / Molar mass = 15 g / 32 g/mol

Next, use Avogadro's number to find the number of oxygen molecules:

Number of oxygen molecules = Number of moles of oxygen * Avogadro's number = (Number of moles of oxygen) * 6.022 × 10^23 molecules/mol

Calculate each part separately, then multiply the number of moles by Avogadro's number to get the final answer.

Remember to substitute the relevant values into the equations and perform the calculations using a calculator or software to get the precise values.