Chemistry-Density and Dimensional Analysis

Question

1.How much space would a 2.34 g sample of a substance occupy, if it has a density of 0.993 g/cm3?

Round answer to 2 decimal places.

2.How many m3 are in 45.7 acres? (1 hectare = 1.0 X 104 m3; 1 hectare = 2.47 acres;)

Use dimensional analysis to solve this problem. Round answer to a whole number.

I have been having trouble focusing and learning in chemistry class and I need help. If you could use these problems to teach me i would greatly appreciate it

Answer 1

Recall that density = mass/volume. So given the mass and the density, you can find the volume. Given the mass and volume, you can find the density. And given the volume and density, you can find the mass.

1). 2.34 g x 1 cm³ / 0.993 g = 2.36 cm³ which is the volume (space) asked for

2). To use dimensional analysis, you simply take what is given to you and use the units so that they cancel each other and you end up with the units you want. A simple example would be converting feet to inches.

If you had 8 feet and wanted to know how many inches that is, you could use dimensional analysis like this:

8 feet x 12 inches / 1 foot = 96 inches (note how feet/foot cancel each other and you are left with inches).

For the problem at hand we have...

45.7 acres x 1 hectare / 2.47 acres x 1.0x10⁴ m³ / 1 hectare = 1.85x10⁵ m³

(note how acres cancel, and hectare cancel, leaving you with m³