How many moles are in 1.45 x10^23 molecules of ammonium phosphate?

Answer 1

Hello, Bre,

I note that you've posted a long list of questions, all pertaining to the mole. I can'rt answer them all, but hope to explain the concept thoroughly enough with this question to demonstate how the others may be answered.

These are all problems that involve the use of conversion factors. A conversion factor has one goal: to change the units of a numer, without changing the underlying value. Let's look at some conversion factors:

12 in a dozen: 12/dozen

12 inches in a foot: 12 in./ft

5.879x10¹² miles/lightyear

1 femptometer/1x10^-15meter

The first two are familar. The second two start illustrating the desire to invent units that make it easier to describe things. Even a science nerd reaches a point when writing 5.879x10¹² miles is a lot less exciting than simply stating 1 lightyear. So nicknames are given to numbers that have find repetitive use, to simply make life easier for thise working with them, and for publishers and readers who don't understand scientific notation.

[I don't remember the actual name, but an MIT student who I'll call Ralph, was chosen by a few of his classmates to be a new unit of measure. Ralph was used to measure the length of the Longfellow Bridge across the Charles River in Cambridge, MA and the group declared the bridge to officially be 153 ralphs long.]

There are a couple of features about conversion units that are especially useful to remember:

1. Conversion factors have a value of 1, since the top and bottom are equivalent. Yes, there are still numbers, e.r., 12.dozen, but the top and bottom are equivalent. So we can multiply a conversion factor by anything and it will still be a valid value. The numbers may change, but so do the units, so the result is a valid number. For example: 1.5 dozen eggs times 12 eggs/dozen equals 18 eggs.
2. Conversion factors can be inverted. If 12 inches = 1 foot, we can state that in two ways:
3. 12 inches/foot, or
4. 1foot/12 inches

Remebering these two features makes conversions a lot easier. In this and the other questions you asked, the unit mole is invlolved. Mole is a defined count of the number of an object. In science, it is typically atoms and molecules. The mole is:

1 mole = 6.02x10²³ items/particles/molecules/etc.

A mole is shorthand for 6.02x10²³ of anything. It is clearly easier, and more fun, to write mole that the actual number. So the conversion factor is:

6.02x10²³ particles/mole, or

1 mole/6.02x10²³ particles

6.02x10²³ atoms of anything may seem like a waste of time. But this number ties closely with the atomic masses of the elements on the periodic table. The atomic mass of an element is typically read as atomic mass units (amu). But these same numbers can also re read as the molar mass" of the element. Molar mass is defined as grams/mole. This means that if you take the atomic mass of any element, you can simply repeat that number and change the unit to grams/mole. It means that if you take that number of grams of an element, you would have 6.02x10²³ atoms of that element. Hard to imagine, but true.

The huge benefit is when you need to decide what masses should be used in a reaction. A balanced equation holds, as written, for exactly the number of atoms or molecules that are shown.

2H₂ + O₂ = 2H₂O

This requires 1 oxygen molecule and 2 hydrogen molecules to make 2 waters molecules. This would mean that someone should count out individual atoms. That would take some very, very, very ting tweezers and a lot, I mean lots and lots of time. We can read the equation in terms of moles: 2 moles of hydrogen plus 1 moke of oxygen makes one mole of water. Now we can weight out grams of each reactant and know that we'll have the porportions of actual molecules that we need for a balanced, and efficient reaction.

The molar mass of H₂ is the two H amu's added to get 2 grams/mole. Two grams of H₂ will contain 6.02x10²³ molecules of hydrogen. We need 4 grams to get 2 moles. Oxygen's molar mass is (2*16 =32 grams/mole).

Back to this question:

How many moles are in 1.45 x10^23 molecules of ammonium phosphate?

Use the conversion factor for a mole: (1 mole/6.02x10²³ molecules)

Multiply times the number of ammonium phosphate (AP) molecules:

(1.45x10²³ AP molecules)*(1 mole/6.02x10²³ molecules) = 0.241 moles AP

=======

The other problems you posted can be answered with the use of conversion factors as was described here. The only additonal work need is to calculate the molar masses of some of the compounds, to generate a grams/mole for that compound.

I hope this helps,

Bob