Question

how many atoms are in 4.0 moles of sodium, na?
? × 10^? atoms na
remember, 1 mol = 6.02 × 10^23 particles
put the coefficient in the green box and the exponent in the yellow box. remember significant figures!

Explanation:

Step1: Identify the conversion factor

We know that 1 mole of any substance contains \(6.02\times 10^{23}\) particles (atoms in this case for sodium). So the conversion factor is \(\frac{6.02\times 10^{23}\text{ atoms Na}}{1\text{ mol Na}}\).

Step2: Multiply moles by conversion factor

We have 4.0 moles of Na. So we multiply the number of moles by the conversion factor:
\(4.0\text{ mol Na} \times \frac{6.02\times 10^{23}\text{ atoms Na}}{1\text{ mol Na}}\)
The moles unit cancels out, and we calculate \(4.0\times6.02\times 10^{23}\).
First, calculate \(4.0\times6.02 = 24.08\).
So we have \(24.08\times 10^{23}\) atoms Na. But we need to express this in scientific notation. In scientific notation, a number is written as \(a\times 10^{n}\) where \(1\leq a< 10\). So we rewrite \(24.08\times 10^{23}\) as \(2.408\times 10^{24}\) (since \(24.08 = 2.408\times 10^{1}\), so \(24.08\times 10^{23}=2.408\times 10^{1}\times 10^{23}=2.408\times 10^{24}\)). Considering significant figures, 4.0 has two significant figures, so our answer should have two significant figures. So \(2.4\times 10^{24}\) (wait, 4.0 has two significant figures, 6.02 has three. When multiplying, the result should have the same number of significant figures as the least precise measurement. 4.0 has two, so \(4.0\times6.02 = 24.08\), which we round to 24 (but in scientific notation, with two significant figures, it's \(2.4\times 10^{1}\), so when multiplied by \(10^{23}\), it's \(2.4\times 10^{24}\)? Wait, no: \(4.0\times6.02\times 10^{23}=24.08\times 10^{23}\). To put in scientific notation: \(24.08\times 10^{23}=2.408\times 10^{24}\). Now, 4.0 has two significant figures, so we round 2.408 to 2.4 (two significant figures). So the coefficient is 2.4 and the exponent is 24.

Wait, let's check again. The formula is: number of atoms = moles × Avogadro's number. So \(n = N\times N_A\), where \(n\) is moles, \(N\) is number of atoms, \(N_A = 6.02\times 10^{23}\text{ mol}^{-1}\). So \(N=4.0\text{ mol}\times6.02\times 10^{23}\text{ atoms/mol}=24.08\times 10^{23}\text{ atoms}\). Now, convert to scientific notation: \(24.08\times 10^{23}=2.408\times 10^{24}\). Since 4.0 has two significant figures, we round 2.408 to 2.4 (two significant figures). So the coefficient is 2.4 and the exponent is 24.

Answer:

The coefficient (green box) is \(2.4\) and the exponent (yellow box) is \(24\), so the number of atoms is \(\boldsymbol{2.4\times 10^{24}}\) atoms Na.