# Suppose a thin sheet of zinc containing 0.2 mol of the metal is completely converted to zinc oxide, #"ZnO"#, in one month. How would you express the rate of conversion of the zinc?

##### 1 Answer

Here's what I got.

#### Explanation:

Unless the question is incomplete, all you really have to do here is pick a unit of *quantity* and a unit of *time* and use the information given to express the rate at which zinc metal,

For starters, you know that **moles** of zinc metal are completely converted to zinc oxide in **one month**.

If you were to stick with *moles* and *months*, you can say that the rate at which zinc is concerted is

#"rate" = "0.2 mol month"^(-1)#

This means that **with every passing month**, you will convert **moles** of zinc to zinc oxide.

Alternatively, you can pick any other unit of time you want. For example, the **same rate** can be expressed as

#0.2color(white)(a)"moles"/color(red)(cancel(color(black)("month"))) * (1color(red)(cancel(color(black)("month"))))/"4.35 weeks" = 0.046color(white)(a) "mol"/"week"#

Therefore, you will have

#"rate" = "0.046 mol week"^(-1)#

Another possibility would be to use *grams* and *seconds*. Convert moles to grams first by using zinc's **molar mass**

#0.2 color(red)(cancel(color(black)("moles Zn"))) * "136.3 g"/(1color(red)(cancel(color(black)("mole Zn")))) = "27.26 g"#

You could use *seconds* instead of *months* to get

#1 color(red)(cancel(color(black)("month"))) * (4.35 color(red)(cancel(color(black)("weeks"))))/(1color(red)(cancel(color(black)("month")))) * (7color(red)(cancel(color(black)("days"))))/(1color(red)(cancel(color(black)("week")))) * (24color(red)(cancel(color(black)("hours"))))/(1color(red)(cancel(color(black)("day")))) * (60color(red)(cancel(color(black)("min"))))/(1color(red)(cancel(color(black)("h")))) * "60 s"/(1color(red)(cancel(color(black)("h")))) = "2,630,880 s"#

This means that the rate of the conversion can be expressed as

#"rate" = "27.26 g"/"2,630,880 s" ~~ 1 * 10^(-5)"g s"^(-1)#

As you can see, you can basically use any unit of time you want to express the rate of conversion, provided of course that a unit is not specified to you.