Chemistry Dimensional Analysis 9 Part question

Question

1.Density is defined as the ratio between a substance's mass and volume. The density of gold is 19.3 g/mL. Explain how density can be used as a conversion factor. What two physical properties of gold can we use density to convert between?

2.Using dimensional analysis, find the volume of 7.50 grams of aluminum. 

3.A student wanted to find the volume in millilieters of 15.75 grams of mercury using dimensional analysis. They reported the following work and answer. Analyze their work and report to them what they did wrong. 

(7.6 g / mL ) x 15.75 g = 301, 079.7 grams

4.The Mole concept is incredibly important in chemistry as it allows us to convert between the molecular (micro ) scale and the macro scale. The Mole is a counting term just like the word dozen. As we already know, the word dozen represents 12 and can be applied to any substance we are counting. The Mole represents 6.022 x 10^23 and can be applied to any susbtance we are counting. Write 4 conversion factors from the two equalities in this question. 

5.Use dimensional analysis to show how many dozens bagels are in 3 thousands bagels

Answer 1

I will answer number 2 and then number 1. For dimensional analysis, create a table like this.

7.50 g Al. | 1 mL First, we add our given, 7.50 g Al. Next we take our density, 19.3 g/mL.

|. 19.3 g. Always make sure you can cancel out units. As you see, we have g on the top of the fraction and on the bottom, therefore we can cancel out the g (grams). Next, calculate the fraction from the table. The fraction is now (7.50*1 mL) / 19.3. Note that we have cancelled out g Al from our equation and we are left with mL (volume). Therefore, 7.5/19.3= 0.389, giving us 0.389 mL of Al.

This is the basis of dimensional analysis. Always make sure you can balance the units on the top and bottom.

We also found the answer to number one: Looking at the units for density, it is given as g/mL (grams per milliliter). As you've seen in the dimensional analysis above, we can interconvert between grams and milliliters.

#3: This is an incorrect use of dimensional analysis. If we set up another table like we did above, we will see that the grams are both in the numerator of the fraction. This is wrong. To convert units, they must be on the numerator and denominator, balancing the two. Furthermore, we are looking for the volume Hg, which is in mL. The answer given is in grams, which is not a unit of volume.

#4: We can use the mole in dimensional analysis as well, remembering that 1 mole=6.022x10²³ molecules (just like one dozen eggs is 12 eggs). We could set up a problem such as "Hoe many molecules are in 2 moles of carbon?"

2 moles carbon |. 6.022x10²³ molecules Moles of carbon can cancel (since they both top and bottom)

|. 1 mole carbon

Therefore, (2*6.022x10²³ molecules)/1= 12.044x10²³, or 1.2044x10²⁴ molecules.

#5: 3000 bagels |. 1 dozen bagels

12 bagels Bagels can cancel out, so we are left with 3000/12= 250 dozen

I hope this helps, let me know if you need anything else!