Convert J/mol k into atm cm^3/mol k

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In summary, my lecturer asked us to convert the ideal gas law into the units "atm cm^3/ mol k" and I'm not sure how to do it.
  • #1
Mr-Thirty
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1
Homework Statement
Convert the ideal gas constant to atm cm^3/ mol k
Relevant Equations
1 J = Nm
1 atm = 101325 Pa
1 m^3 = 1 x 10^6 cm^3
My lecturer asked us to convert the ideal gas law into the units "atm cm^3/ mol k"
I've used conversion brackets before and I am comfortable converting things like mile/gallon to km/litre but I don't understand how to do this one.
The way I was taught was to put the units in brackets and take the numerical calculation out to the front. Then find the conversion and place them in the brackets such that they cancel with the original units and leave behind the new units you were after.

i.e. For 3 feet into inches: 3 x [ft x 12 inch/ 1 ft], the ft's cancel and you do 3 x 12 = 36 inches

But for converting J / mol k to atm / mol k I am not sure what to do. I know these are the conversion factors:

1 J = Nm
1 atm = 101325 Pa
Pa = N/m^2
1 m^3 = 1 x 10^6 cm^3

But I am trying to reconcile how Joules can be expressed in terms of pressure x volume. I know I need to find an expression for Joules which I can place on the bottom of the fraction in order to cancel it. I think its the idea of the volume part of the calculation which I can't get my head around. I don't know how to express force x distance, force x area and pressure x volume.

(8.314) x [ (J / mol k) x (atm / 101325 Pa) x (cm^3 / m^-3) ]

(8.314) x [ (Nm / mol k) x (atm / 101325 Nm^-2) x (cm^3 / m^-3) ]

How can I express this so I can cancel? Whats the best way to write this?
 
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  • #2
Start from the well known value ##R = 8.31~\mathrm{\frac{J}{mol\cdot K}}##. It looks like you need to convert 1 J into some number times ##\mathrm{atm \cdot cm^3}## because the two are dimensionally the same. Express all units in terms of the basic kilograms, meters and seconds. For example, 1 Newton = 1 kg m/s2.
 
Last edited:
  • #3
kuruman said:
Start from the well known value ##R = 8.31~\mathrm{\frac{J}{mol\cdot K}}##. It looks like you need to convert 1 J into some number times ##\mathrm{atm \cdot cm^3}## because the two are dimensionally the same. Express all units in terms of the basic kilograms, meters and seconds. For example, 1 Newton = 1 kg m/s2.

Thank you for the reply, so I tried expressing Joules and pascal in terms of their basic units and I am still getting the wrong units. I know the answer is around 82 but i don't know why my units are still wrong. Is it my algebra? I can't see what's wrong
 

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  • #4
Two mistakes
First: 1 Pa = 1 N/m2 not 1 kg/m2. You need to convert the Newton unit into kg - m - s units.
Second: Where does the extra factor ##\mathrm{\frac{10^{-6}cm^3}{m^3}}## come from? Just convert all meters into centimeters after canceling like terms in the numerator and denominator.
 
  • #5
Ok thanks for your help, I think I may have figured it out. Please check my working below
 

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  • #6
That looks about right. :oldsmile:
 
  • #7
kuruman said:
That looks about right. :oldsmile:
Thank you so much
 

1. What is the formula for converting J/mol K into atm cm^3/mol K?

The formula for converting J/mol K into atm cm^3/mol K is: 1 J/mol K = 0.08314472 atm cm^3/mol K.

2. Why do we need to convert between these units?

Converting between units allows us to express the same quantity in different units, making it easier to compare and understand measurements. In this case, J/mol K is a unit of energy per mole of substance, while atm cm^3/mol K is a unit of pressure times volume per mole of substance. Converting between these units can help us better understand the relationship between energy, pressure, and volume in a system.

3. How do I convert J/mol K into atm cm^3/mol K?

To convert J/mol K into atm cm^3/mol K, simply multiply the value in J/mol K by 0.08314472. This will give you the equivalent value in atm cm^3/mol K.

4. Can I use a calculator to convert between these units?

Yes, you can use a calculator to convert between these units. Simply enter the value in J/mol K and multiply it by 0.08314472 to get the equivalent value in atm cm^3/mol K.

5. Are there any other units that can be converted into J/mol K or atm cm^3/mol K?

Yes, there are other units that can be converted into J/mol K or atm cm^3/mol K. Some common units include joules per mole per kelvin (J/mol K), kilojoules per mole per kelvin (kJ/mol K), and calories per mole per kelvin (cal/mol K). It is important to pay attention to the units when converting between different systems of measurement.

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