Finding the mass of a mixture?

mass Na = 0.73 g

moles Na = 0.73 g x (1 mole Na / 22.98 g) = 0.0318 moles

now let's say moles Na in NaCl = X

in which case moles Na in NaBr = (0.0318 - X)

since the ratios of Na to Cl and Na to Br is 1:1..

moles Cl = X

moles Br = (0.0318 - X)

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now we know total mass = 2.08 g... and of that 0.73 g is Na.. so 2.08 - 0.73 = 1.35 g.... and that must be the mass of Cl + Br.. right?

and since moles x (g / mole) = grams...

mass Cl + mass Br = 1.35g

moles Cl x (molar mass Cl ) + mass Br x (molar mass Br) = 1.35

or

X * (35.45) + (0.0318 - X) * 79.90 = 1.35

35.45 X + 2.54 - 79.90X = 1.35

-45.45 X = -1.19

X = 0.0268 = moles Na in NaCl

and

(0.0318 - X) = 0.0050 = moles Na in NaBr..

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again, since the ratio of Na to Cl and Na to Br is 1:1....

moles NaCl = 0.0268

moles NaBr = 0.0050

follow all of that?

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finally....

mass NaCl = 0.0268 moles x (58.45 g / mole) = 1.56 g

mass NaBr = 0.0050 moles x (102.9 g / mole) = 0.52 g

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let's check... 1.56 + 0.52 = 2.08.. that works...

0.0268 moles NaCl x (1 mole Na / 1 mole NaCl) x (23 g Na / mole Na) = 0.615 g

0.0050 moles NaBr x (1 mole Na / 1 mole NaBr) x (23 g Na / mole Na) = 0.115 g

0.0615 g + 0.115 g = 0.73 g....of Na....

and that checks out....

Questions?

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I'm not a chemist fyi. just a lowly lowly chemical engineer. :).. The chemist made a mistake by assuming 1/2 of the Na was in NaCl and 1/2 in NaBr... that is an incorrect assumption.

what is true is that the total number of Na atoms = atoms Cl + atoms of Br.... but atoms of Cl ≠atoms of Br

To answer this question, one needs a periodic table. The table lists all the elements, and more importantly, the atomic weights. The atomic weight of Sodium (Na) is 23 grams per mole. A "mole" is a number which chemists use to express weight (or mass). 1 mole of Sodium atoms weighs about 23 grams.

Also:

1 mole of Chlorine (Cl) atoms weighs 35.5 grams

1 mole of Bromine (Br) atoms weighs 80 grams

Now, if there are 0.73 grams of Sodium, this is (0.73 gm)/(23 gm/mole) = 0.0317 moles of Sodium.

Next, note the chemical formulas. For every Chlorine and every Bromine atom, there is a Sodium atom. This means half the moles of Sodium is equivalent to the moles of either Bromine or Chlorine. To express weight, just multiply the moles of either by the atomic weight:

(0.0317 moles/2)*(35.5 gr/mole Cl) = 0.56 grams Cl

(0.0317 moles/2)*(80 gr/mole Br) = 1.26 grams Br

1.26 gm Br + (0.0159 moles)*(23 gm Na/mole) = 1.62 gm NaBr

PROOF : ???

0.56 gm + 1.26 gm + 0.73 gm = 2.56 grams

This is 0.48 grams heavier than the 2.08 grams stated.