Kyle R.

asked • 03/23/16

How many salt molecules are in one grain of salt?

A grain of salt ( NaCl) has a mass of about 0.3mg. How many NaCl molecules are there in one grain of salt?

Salin T.

In one grain of salt, based on the numbers you provided, I got that there were 3.09 x 1018 particles (molecules) of NaCl. The calculations were done by using the conversion of grams to moles to particles.
 
First, I converted the 0.3mg of NaCl into 0.0003g of NaCl. This was done because molar mass is in units of g/mol. Then, I found the molar mass of NaCl and found it to be 58.44 g/mol. I then used the value of 0.0003g of NaCl and divided it (or multiply by 1 mol / 58.44g) by the molar mass of NaCl, so as to cancel out the grams and be left with the moles of NaCl present in one grain of salt. This number came out to be 5.13347022588 x 10-6 mol NaCl in 0.0003g NaCl. The next step in the process is to convert moles into particles (atoms, molecules, etc.). Based on Avagadro's number, there are 6.022 x 1023 particles in every one mole of substance. So I multiplied the moles of NaCl (5.133... x 10-6 moles) by Avagadro's number and got the answer: one grain of salt ≈ 3.09 x 1018 molecules. Hope this helped mate!
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03/23/16

1 Expert Answer

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Carol E. answered • 03/24/16

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Kyle,
 
The path to follow here is to convert mg--> grams---->moles--->molecules.
 
0.3 mg (1 gram/1000 mg) = 0.0003 gram NaCl
 
0.0003 g NaCl (1 mole NaCl/58.44 g) = 0.0000051 mol NaCl    (58.44 is the molar mass of NaCl)
 
0.0000051 mol NaCl (6.02 ^23 molecules/mole) = 3.09 ^18 molecules of NaCl
 
To the correct number of sig figs, the answer is 3 ^18 molecules.
 
This problem is an example of dimensional analysis and the use of conversion factors.
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