What would be the mass of $4.5 \times 10^{26}$ $4.5xx10^26$ carbon atoms?

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What would be the mass of $4.5 \times 10^{26}$ $4.5xx10^26$ carbon atoms?

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Answer 1 · 2017-05-18T12:38:09

Well, the mass of $6.022 \times 10^{23}$ $6.022xx10^23$ carbon atoms is $12.011 \cdot g$ $12.011*g$ .

Explanation:

How do we know this? Well, $6.022 \times 10^{23}$ $6.022xx10^23$ individual $^{12} C$ $""^12C$ atoms has a mass of $12.00 \cdot g$ $12.00*g$ precisely, and we use this number as a bridge between the sub-micro world of atoms and molecules to the macro world of grams, and litres, that which we can quantitatively measure.

And so.........

$Mass of carbon = \frac{4.5 \times 10^{26} \cdot carbon atoms \times 12.011 \cdot g}{6.022 \times 10^{23} \cdot carbon atoms}$ $"Mass of carbon"=(4.5xx10^26*"carbon atoms"xx12.011*g)/(6.022xx10^23*"carbon atoms")$

$≅ 9 \cdot k g$ $~=9*kg$ carbon...........

Answer 2 · 2017-05-18T12:42:05

We will convert to mols.

Explanation:

1 mol of $C$ $C$ has 6.02xx10^23 atoms (Avogadro's number).

So the number you mention contains:

$\frac{4.5 \times 10^{26}}{6.02 \times 10^{23}} = 0.748 \times 10^{3} m o l$ $(4.5xx10^26)/(6.02xx10^23)=0.748xx10^3mol$

Since 1 mol of $C$ $C$ has a mass of $12.01 g$ $12.01g$

Total mass $= 12.01 \times 0.748 \times 10^{3} = 8.98 \times 10^{3} g \approx 9.0 k g$ $=12.01xx0.748xx10^3=8.98xx10^3g~~9.0kg$

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What would be the mass of $4.5 \times 10^{26}$ $4.5xx10^26$ carbon atoms?

2 Answers

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