Question

1. the polypropylene cubes have a density of 0.946 grams per milliliter. identify the true statement(s). select all that apply. a. the cube floats on water because the water’s density is greater than the cube’s density. b. the cube sinks in methanol because methanol’s density is less than the cube’s density. c. the cube floats on 1,2 - dichloroethane because the cube’s density is greater than 1,2 - dichloroethane’s density. d. the cube sinks in methanol because methanol’s density is greater than the cube’s density. 2) which liquid(s) could be used for displacement? select all that apply. a. methanol b. water c. 1,2 - dichloroethane

Explanation:

Step1: Recall density - float/sink rules

An object floats in a liquid if the object's density ($
ho_{object}$) is less than the liquid's density ($
ho_{liquid}$), and sinks if $
ho_{object}>
ho_{liquid}$. The density of water is approximately 1 g/mL, the density of methanol is approximately 0.79 g/mL, and the density of 1,2 - dichloroethane is approximately 1.24 g/mL. The density of the polypropylene cube is 0.946 g/mL.

Step2: Analyze option A

Since $
ho_{cube}=0.946$ g/mL and $
ho_{water}\approx1$ g/mL, $
ho_{cube}<
ho_{water}$, so the cube floats on water. Option A is correct.

Step3: Analyze option B

Since $
ho_{cube}=0.946$ g/mL and $
ho_{methanol}\approx0.79$ g/mL, $
ho_{cube}>
ho_{methanol}$, so the cube sinks in methanol. Option B is correct.

Step4: Analyze option C

Since $
ho_{cube}=0.946$ g/mL and $
ho_{1,2 - dichloroethane}\approx1.24$ g/mL, $
ho_{cube}<
ho_{1,2 - dichloroethane}$, so the cube should float, but the reasoning in option C is wrong. The cube floats because its density is less than that of 1,2 - dichloroethane, not greater. So option C is incorrect.

Step5: Analyze option D

As $
ho_{cube}>
ho_{methanol}$, the cube sinks in methanol, but the reasoning in option D (saying methanol's density is greater) is wrong. So option D is incorrect.

Step6: Determine liquids for displacement

Liquids that can be used for displacement are those in which the object sinks. Since the cube sinks in methanol, methanol can be used for displacement. Water and 1,2 - dichloroethane, in which the cube floats, are not suitable for displacement as the cube will not displace its full - volume of these liquids.

Answer:

1. A. The cube floats on water because the water’s density is greater than the cube’s density, B. The cube sinks in methanol because methanol’s density is less than the cube’s density
2. A. Methanol