Physical Chemistry-Gas Laws (Find R and M)

In summary, the question asks for the calculation of the gas constant R and the molar mass of oxygen using data obtained from the Atkins Physical Chemistry text, 9th Edition. Using the formula R= (Vm P)/ T and extrapolating back to when p=0, the value of R was found to be 0.0820614 dm^3 atm/K mol. However, there is no clear method to calculate the molar mass from the given data, as the absence of density makes it difficult to use equations such as Vm= M/ density = RT/P= V/n. It is possible that this is an error in the book.
  • #1
bluegreen
2
0
Thanks ahead of time for any help!

Homework Statement


From Atkins Physical Chemistry text, 9th Edition:
1.7b) The following data has been obtained for oxygen gas at 273.15 K. Calculate the best value of the gas constant R from them and the best value of the molar mass of O2 (oxygen).

p(in atm)
P1=0.750 000
P2= 0.500 000
P3=0.250 000

Vm [molar volume] (in dm^3/mol)
Vm1= 29.8649
Vm2=44.8090
Vm3=89.6384

Homework Equations


The Attempt at a Solution



To find R, I used R= (Vm P)/ T to find the different Rs for each set of data, then used y=mx+b (using data points [P, R]) to extrapolate back to when p=0 (when ideal gas is most accurate; so that means the y intercept which was equivalent to R).

I know you can just graph it and get the same result. Either way, I got R= 0.0820614 dm^3 atm/K mol.

Now I'm lost. How do I set it up to find molar mass? Do I extrapolate using a graph again? I'm not given density, so it throws a wrench in a lot of the equations I tried using, like:
Vm= M/ density = RT/P= V/n
 
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  • #2
No idea - I can't think of any approach that will let calculate molar mass from the given data.

That's to let you know someone actually read your post and spend a moment thinking how to help.

It can always be an error in the book. I can be also missing something.
 
  • #3
Thanks. I know that in the old editions, density is given, but density was omitted for the 9th edition. Not sure if it was a mistake or if it was to make the question trickier!
 
  • #4
Must be mistake then.

--
 
  • #5
RT.

Hello,

To find the molar mass (M) of oxygen, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. We can rearrange this equation to solve for the molar mass M:

M = (mRT)/PV, where m is the mass of the gas in grams.

To find m, we can use the density equation d = m/V, where d is the density, m is the mass, and V is the volume. We can rearrange this equation to solve for m:

m = dV.

Substituting this into the equation for M, we get:

M = (dVRT)/PV.

Now, we can use the data given to solve for M:

P1 = 0.750 atm, V1 = 29.8649 dm^3/mol
P2 = 0.500 atm, V2 = 44.8090 dm^3/mol
P3 = 0.250 atm, V3 = 89.6384 dm^3/mol
T = 273.15 K

Substituting these values into the equation for M, we get:

M = [(d)(29.8649 dm^3/mol)(0.0820614 dm^3 atm/K mol)(273.15 K)]/[(0.750 atm)(29.8649 dm^3/mol) + (0.500 atm)(44.8090 dm^3/mol) + (0.250 atm)(89.6384 dm^3/mol)]

Simplifying, we get:

M = [(d)(7.7737 dm^3 atm K mol)]/[(22.3987 dm^3/mol) + (22.4045 dm^3/mol) + (22.4096 dm^3/mol)]

M = (d)(0.3462 dm^3 atm K mol)

Now, we need to find the density (d) of oxygen at 273.15 K. We can use the ideal gas law equation again, but this time for a single set of data (P1 = 0.750 atm, V1 = 29.8649 dm^3/mol):

d = (P1M)/(RT) = [(0.750 atm)(0.0820614
 

Related to Physical Chemistry-Gas Laws (Find R and M)

1. What is the ideal gas law and how is it derived?

The ideal gas law is a fundamental equation in physical chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is derived from combining Boyle's law, Charles's law, and Avogadro's law.

2. What is the value of the gas constant (R) and how is it used?

The gas constant (R) is a proportionality constant that relates the properties of gases in the ideal gas law. Its value depends on the units used, but the most commonly used value is 0.0821 L·atm/mol·K. It is used to convert between different units of pressure, volume, temperature, and moles in the ideal gas law equation.

3. How do you calculate the molecular weight (M) of a gas using the ideal gas law?

The molecular weight (M) of a gas can be calculated using the ideal gas law by rearranging the equation to solve for M. The equation is M = (mRT)/PV, where m is the mass of the gas in grams, R is the gas constant, T is the temperature in Kelvin, P is the pressure in atmospheres, and V is the volume in liters.

4. What is the difference between real and ideal gases?

An ideal gas is a theoretical concept that follows the ideal gas law exactly, meaning it has no intermolecular forces and occupies no volume. Real gases, on the other hand, have intermolecular forces and take up some volume, causing deviations from the ideal gas law at high pressures and low temperatures.

5. How do you use the ideal gas law to solve problems involving gases?

To use the ideal gas law to solve problems, you first need to identify the variables given and the variable you are trying to solve for. Then, rearrange the equation to solve for the desired variable and plug in the given values. Be sure to convert all units to the appropriate units (atm, L, K, mol) before solving.

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