# A mixture of two gases has a total pressure of 5.7 atm. If one gas has a partial pressure of 4.1 atm, what is the partial pressure of the other gas?

##### 1 Answer

I got

**DALTON'S LAW OF PARTIAL PRESSURES**

The equation that sums up what we have to do in this problem (pun intended) is **Dalton's law of partial pressures**:

#\mathbf(P_"tot" = sum_(i=1)^(N) P_i)#

#= P_1 + P_2 + . . . + P_N#

which really says that the **total pressure** is the sum of all the individual pressures, known as *partial pressures*.

(Note that this equation is constructed for ideal gases only, so it doesn't work perfectly for real gases.)

**USING DALTON'S LAW OF PARTIAL PRESSURES**

By the language of the question, we already know that there are only **two** gases in the closed container; let's call them gas

So, from the question, what we have at our disposal, and what we are solving for, are:

#P_"tot" = "5.7 atm"#

#P_1 = "4.1 atm"#

#P_2 = ???#

Therefore, the unknown partial pressure is:

#color(blue)(P_2) = P_"tot" - P_1#

#= 5.7 - 4.1#

#=# #color(blue)("1.6 atm")#

**UNSTATED ASSUMPTIONS IN THE PROBLEM**

When we are looking at **ideal gases**, we can say that their partial pressure *contributions* are similar at any total pressure for any identity gas. (This is not true for real gases.)

Another unstated assumption is that this is a *closed rigid container*, so we have a **constant volume**. That allows us to assume that the pressures are *additive* (but that still doesn't entirely work unless the gases are truly ideal).