# How do you convert 0.505 moles of Ti to grams?

Nov 28, 2016

24.2 grams of titanium.

#### Explanation:

You have been given 0.505 moles of titanium, and you need to convert this quantity of the metal into a mass.
Titanium has 47.867 grams for each mole, as listed on the periodic table. This information is vital because it houses the conversion factor for this problem. You may even see that you can estimate the answer, based off the given information. Approximately a half mole is going to be about 24 grams, based on an approximated 48 grams of titanium for each mole. But we need to work out the math just to be sure.

The conversion factor that you'll use for this problem, and many others that are similar to it, is the ratio of the number of grams of a substance per mole ($\frac{g}{m o l}$) or its inverse, moles per gram ($\frac{m o l}{g}$). Both are correct, because they are both equal, but it's important for you to determine which one to use.

Knowing that you have 0.505 moles of titanium means that this is the value you should start your problem with. Since you're wanting to know the mass, in grams, of titanium in the end, that's where you'll end. You should use this information to help plan your mathematical approach, via setting up your dimensional analysis.

• $0.505 m o l$ $\to$ $\frac{g r a m s}{m o l}$

• $0.505 m o l$ $\to$ $\frac{m o l}{g r a m s}$

Since your final units need to be in grams, there is only one of two possibilities that could make sense. If you thought to yourself that it's the second one, you're right! The first one is wrong because your final units would be ${\left(m o l\right)}^{2} / \left(g r a m s\right)$. Those units don't make any sense.

Now, let's do the math:

$0.505 m o l$ $X$ $\frac{g r a m s}{1 m o l}$ $\approx$ $24.172835$ $g r a m s$

This is true because the moles units cancel each other out, because any time you divide something by itself, it's equal to 1, and the number 1 is always implied in multiplication. So, you're left with grams, which is what you want.

There is still one final step. We have to account for significant figures, since the answer of 24.172835 isn't expected to be accurate. We're only as accurate as our smallest value (in terms of numbers of significant figures), which is 0.505. This has 3 significant figures.
Because of this, the final value is $\approx 24.2$ grams of titanium.