Biehle's Nova Physics page 3 error with volume calculation?

[thatrunner]

1. The problem statement, all vbles and given/known data

So I'm going through the Nova Physics book and I'm wondering if there's a mistake in calculation. The question reads: How much volume does 0.4kg of oxygen gas take up at T= 27 degrees Celsius and P= 12 atm (gas constant R = 0.0821 L atm/ K Mol).

Homework Equations

V= nRT/ P
the text's last two steps for this calculation are: 0.4x1000x0.08x300 / 32 x 12
the last calculation is: 4x8x300 / 8x50 giving an answer of 24 L.
Where on Earth did the 8x50 denominator come from?

The Attempt at a Solution

I keep coming up with 25L, but the textbook calculates the volume to be 24L.


Thanks in advance for any help offered :)

 

[Andrew Mason]

1. The problem statement, all vbles and given/known data

So I'm going through the Nova Physics book and I'm wondering if there's a mistake in calculation. The question reads: How much volume does 0.4kg of oxygen gas take up at T= 27 degrees Celsius and P= 12 atm (gas constant R = 0.0821 L atm/ K Mol).

Homework Equations

V= nRT/ P
the text's last two steps for this calculation are: 0.4x1000x0.08x300 / 32 x 12
the last calculation is: 4x8x300 / 8x50 giving an answer of 24 L.
Where on Earth did the 8x50 denominator come from?

The Attempt at a Solution

I keep coming up with 25L, but the textbook calculates the volume to be 24L.


Thanks in advance for any help offered :)

It may be a rounding problem. I get 25.6 litres.

If you want to use V = nRT/P you have to use R = 8.3145 Nm/mol K and P in Pascals (N/m) with 1 atm = 101,325 N/m. Volume will be in m^3 so multiply by 1000 to get litres

n = 400g/(32 g/mol) = 12.5 mol
P = 12 x 101,325 = 1,215,900 N/m
T = 300 K
R = 8.3145 J/mol K

V = 1000 x 12.5 x 8.3145 x 300/1.216e6 = 25.6 L.

AM

 

[thatrunner]

Thanks Andrew for taking the time to respond.
Yes, without rounding off the initial figures, I come up with an answer of 25.6 L.
The last stage in calculations in the book confused me when it moved from having a 32x12 denominator to a denominator of 8x50... I think the last step contains a misprint.