# What is the relation between partial pressure and concentration?

So, one of my books said that partial pressure plays more significance in determining the gradient than concentration. So, it said it was possible for a gas to go from high partial pressure at point A to low partial pressure at point B, even though there is low concentration at point A and high concentration at point B.

How is this even possibly? I thought partial pressure and concentration were always related.

• because of temperature. Temperature at A must be more than temperature at B – manshu Dec 1 '15 at 14:33
• This does not really answer my question. :( – kingkong5678 Dec 19 '15 at 15:45

## 1 Answer

MATHEMATICALLY

At point A

The pressure according to ideal gas equation is $P_A = C_ART_A$. Here $C_A (= n/V)$ is concentration at A.

At point B

Similarly, the pressure according to ideal gas equation is $P_B = C_BRT_B$. Here again $C_B$ is concentration at B.

Now, $P_A$ > $P_B$

So, $C_ART_A$ > $C_BRT_B$

i.e. $C_A/C_B$ > $T_B/T_A$ .....equation 1

Now as the condition is that concentration at A is lower than the the concentration at B. Therefore we can say that

$C_A/C_B$ < $1$ .....equation 2

Now from equation 1 and 2 we have

$T_B/T_A$ < $1$

which gives us $T_A$ > $T_B$

So in the end, yes, your book was right. It is possible if the temperature at A is more than that at B.

"HOW TO FIND IT IN SECONDS" or "I HATE TO DERIVE BY USING EQUATIONS"

Think of two containers A and B which are connected by a pipe. Both are connected with the help of a pipe which is closed (i.e. it doesn't let the gases exchange). Now we know that concentration of gas in A is lower than the the concentration of gas in B. If we want more pressure of gas in A then the velocity of its particles should be more. Now it is possible if it has more thermal energy. So the temperature should be more in A.