How many grams of NaCl are needed to produce 500. mL of 1.66 M NaCl solution?

Question

I know that the answer should be 48.6 grams if that helps any.

Answer 1

Ally,

This question must be based on solutions chemistry so I will start there.

The problem gives you the Molarity which means is moles / Liters which means mL will need to be converted into L and grams into moles to keep all units the same.

To convert 500. mL into liters you need the conversion factor which is 1 L = 1000mL.

To successfully complete conversions this is the best method that shows all of the work:

500.mL x (1 L / 1000mL) = (500 x 1) / 1000 = 0.500 L

Since we were given 500 mL, I started with that number and placed the mL on the bottom of the fraction created from the conversion factor so that the mL cancel when they are divided.

Next to convert grams to moles we need to find the molecular mass of NaCl from the periodic table.

The mass of Na is about 22.99 g and Cl is about 35.45 g.

The total mass of NaCl is 22.99 + 35.45 = 58.44 g.

Now we need to use the conversion factor from the definition of a mole : 1 mole NaCl = 58.44 g NaCl

We do not have moles yet so we need to find the moles from using molarity and 0.500L.

To find moles from molarity the equation is : moles = volume (L) x Molarity (moles/L)

So we substitute 0.500 L x 1.66(moles/L) = 0.83 moles NaCl

Now we have moles and can convert them to grams :

0.83 moles x (58.44 g / 1 mole) = (0.83 x 58.44) / 1

48.5052 grams NaCl

Then to make the answer have the correct significant figures we need our answer to have the lowest number of sig figs between 500. and 1.66 from our givens in the problem. They both have 3 sig figs so the answer should be 48.5 grams NaCl. (give or take 0.1 grams due to rounding differences throughout each step)