How would this problem be worked using dimensional analysis? Answer is 1.32g and I can work it (.900/13.6) * 20 = 1.32

But i need it in dimensional analysis and the hint was to first find volume of mercury.

How many grams of alcohol with a density of 0.900 g/cm3 will have the same volume as 20.0 g of mercury, with a density of 13.6 g/cm3?

How about this? volume of Hg is mass/density or in dimensional analysis it is

20g x (1 cc/13.6 g) (g cancels and leaves cc which is volume) of Hg. .
Now we want to convert to grams alcohol.
20 g x (1 cc/13.6 g) x (0.9 g/cc) = ?

cc on top cancels with cc on bottom.
g on top cancels with grams on bottom and leaves a g on top.

To solve this problem using dimensional analysis, we need to determine the volume of the given mass of mercury and then find the mass of the alcohol with the same volume.

We know that the density of mercury is 13.6 g/cm^3, and the mass of mercury given is 20.0 g. To find the volume of mercury, we can use the formula:

Density = Mass / Volume

Solving for volume, we have:

Volume = Mass / Density = 20.0 g / 13.6 g/cm^3

Now, let's use dimensional analysis to determine the mass of alcohol with the same volume. We have the density of alcohol as 0.900 g/cm^3.

We can set up a conversion factor to convert the volume of mercury to the mass of alcohol:

20.0 g of mercury = ? g of alcohol

To set up the conversion factor, we need to cancel out the units of volume (cm^3). From the densities given, we know that:

13.6 g of mercury = 1 cm^3 of mercury

0.900 g of alcohol = 1 cm^3 of alcohol

Multiplying the given mass of mercury by the conversion factor, we get:

20.0 g of mercury * (0.900 g of alcohol / 13.6 g of mercury) = ? g of alcohol

Now, let's cancel out the units:

20.0 g of mercury * (0.900 g of alcohol / 13.6 g of mercury) = (20.0 g * 0.900 g) / (13.6 g) = 1.32 g of alcohol

So, the mass of alcohol with the same volume as 20.0 g of mercury is 1.32 grams.