# How many atoms are in 33 g of titanium (Ti)?

Apr 8, 2017

Approx. $4 \times {10}^{23}$ individual titanium atoms..........

#### Explanation:

We work out the molar quantity of titanium metal:

$\text{Moles of titanium}$ $=$ $\frac{33 \cdot g}{47.9 \cdot g \cdot m o {l}^{-} 1} \cong 0.70 \cdot m o l$

Note that this quotient is dimensionally consistent. We wanted an answer in $\text{moles}$, we got the quotient with units of:

$\frac{\cancel{g}}{\cancel{g} \cdot m o {l}^{-} 1} = \frac{1}{m o {l}^{-} 1} = \frac{1}{\frac{1}{m o l}} = m o l$ as required...... Capisce?

And then we multiply this molar quantity by $\text{Avogadro's number}$, which is $6.022 \times {10}^{23} \cdot m o {l}^{-} 1$ (and the number of titanium atoms has a mass of $47.9 \cdot g$ by definition).

$\text{Number of titanium atoms} = 6.022 \times {10}^{23} \cdot m o {l}^{-} 1 \times 0.7 \cdot m o l$

$\cong 4.0 \times {10}^{23}$