# Question #f5bf1

##### 1 Answer

#### Explanation:

The cool thing about this problem is that you can give a very quick answer by looking in the **periodic table**.

More specifically, take a look at the **molar masses** of chlorine,

#"For Cl: " "35.4527 g mol"^(-1)#

#"For K: " "39.0983 g mol"^(-1)#

This tells you that **every mole** of chlorine will have mass of **every mole** of potassium will have a mass of

Now, take a loo at the compound's **percent composition**.

Notice that you have **approximately** equal amounts of chlorine and potassium **per** **exactly** the same amount of chlorine and potassium **per**

However, since you get slightly **more ** potassium **per mole** than chlorine

#~~"39 g for K "# versus#" "~~ "35.5 g for Cl"#

it makes sense to have a percent composition of potassium that's *slightly higher* than that of chlorine

#"52.7% for K" "# versus#" ""47.3% for Cl"#

This means that the **empirical formula** of the compound **has to be**

#color(green)(|bar(ul(color(white)(a/a)"K"_1"Cl"_1 implies "KCl"color(white)(a/a)|)))#

Now, here's how you can prove this by doing some calculations. Pick a

#"For K: " "52.7 g"#

#"For Cl: " "47.3 g"#

Use the molar masses of the two elements to determine how many **moles** of each you get in this sample

#"For K: " 52.7 color(red)(cancel(color(black)("g"))) * "1 mole K"/(39.0983color(red)(cancel(color(black)("g")))) = "1.348 moles K"#

#"For Cl: " 47.3color(red)(cancel(color(black)("g"))) * "1 mole Cl"/(35.4527color(red)(cancel(color(black)("g")))) = "1.334 moles Cl"#

The **empirical formula** of a compound tells you the **smallest whole number ratio** that exists between its constituent elements. To find that ratio, divide both values by the smallest one

#"For K: " (1.348color(red)(cancel(color(black)("moles"))))/(1.344color(red)(cancel(color(black)("moles")))) = 1.003 ~~ 1#

#"For Cl: " (1.344color(red)(cancel(color(black)("moles"))))/(1.344 color(red)(cancel(color(black)("moles")))) = 1#

Once again, the empirical formula comes out to be

#color(green)(|bar(ul(color(white)(a/a)"K"_1"Cl"_1 implies "KCl"color(white)(a/a)|)))#