A gas law in chemistry says that PV/T=pv/t. Suppose that T=200, t=250,V=6,v=5, P=50. Find p.

Question

A gas law in chemistry says that PV/T=pv/t. Suppose that T=200, t=250,V=6,v=5, P=50. Find p.

Answer 1

All we have to do here is plug each of those numbers into the appropriate place in the given equation. We could also solve for 'p' with just the symbols then plugging in the values. I'll show you both methods.

 

Method 1:

 

50 * 6 / 200 = p * 5 / 250

 

Do the calculations on each side and we find that

 

1.5 = p * 0.02

 

Now divide by 0.02 to solve for p

 

75 = p

 

Method 2:

 

Here, we manipulate the variables themselves. The original equation was

 

PV/T = pv/t

 

and we wanted to solve for p, so we multiply by t and divide by v to get

 

PVt / (Tv) = p

 

Plug in what we know

 

( 50 * 6 * 250 ) / ( 200 * 5 ) = p

 

The order of operations says that we should do the parenthetical operations first, so we get

 

75000 / 1000 = p

 

Which simplifies to 

 

75 = p

 

You can see that we get the same result using either method, so this works out well.

 

I think the major confusion for this problem comes from the upper and lower case letters. They represent different "sets" of data. At first glance, it might seem that the given equation is meaningless because clearly one thing is equal to itself. However, the actual meaning of the equation is that each side of the equation happens to be equal to some other constant. It is like saying that

 

x/y = 5

 

Any combination of x and y that is equal to 5 is also equal to any other combination of x and y that equals 5 (because they're equal to the same value)

 

For example

 

10/2 = 5

 

and x/5 = 5

 

Both left hand sides are equal to 5, so we have

 

5 = 5 (not very useful to us)

and

10/2 = x/5

 

We find that x is 25.  This tangent was not necessary to find the solution, but it is a very important concept to understand. Please let me know if you have any questions about this.