Chemistry Marathon Problem.?

Question

A cylindrical bar of gold that is 1.5 in high and .25 in in diameter has a mass of 23.1984 g, as determined in an analytical balance. An empty graduated cylinder is weighed on a triple beam balance and has a mass of 73.47 g. After pouring a small amount of a liquid into the graduated cylinder, the mass is 79.16 g. When the gold cylinder is placed in the graduated cylinder (The liquid covers the top of the gold cylinder) , the volume indicated on the graduated cylinder is 8.5 mL. Assume that the temperature of the gold bar and the liquid are 86 degrees Fahrenheit . IF the density of the liquid decreases by 1.0% for each 10 degrees Celsius rise in temperature (over the range 0 to 50 degrees Celsius), determine

a) The density of the gold at 86 degrees Fahrenheit
b) The density of the liquid at 40 degrees Fahrenheit

Please show some work and procedure.

Thanks

Hey drutazo, this is not a homework question, I on my winter brake vacation and i;m studying for my ap exam and my chemistry sat subject test, so I'm posting hard questions like this so I can check my answers, and it would really help me if you or anyone else answer it. please

"(the liquid covers the top of the gold bar)"
What would it mean if the liquid didn't cover the top of the gold bar?

Answer 1

Start by calculating the density of the gold at 86 degrees Fahrenheit. This is pretty easy, because you have the dimensions and mass of the cylinder. The volume of a cylinder is just pi*d*h, and you have the diameter d and the height h. However, you will need to convert this to metric, because you've been given the physical dimensions in inches. Just multiply each linear measurement by a conversion factor of (2.54 cm / in) before putting them into the volume formula. Once you have the volume, density is just mass / volume.

Calculating the density of the liquid is more involved. 8.5 mL is the volume of the gold bar and the liquid. You calculated the volume of the gold bar in part a, so now subtract it from 8.5 to get the volume of the liquid, remembering that 1 mL = 1 cm^3. Use the difference in mass of the graduated cylinder, before and after the liquid was poured, to get the mass of the liquid. Then use the density = mass / volume formula again, in order to get the density of the liquid at 86 degrees Fahrenheit.

But the question asks for the density at 40 degrees Fahrenheit. You have information regarding the density of the liquid over ranges of Celcius temperatures, so you must perform another conversion. In this case, remember that a Celcius degree is equal to 1.8 Fahrenheit degrees. The decrease in temperature is 46 degrees Fahrenheit, so divide by 1.8 to get the Celcius temperature change. The statement is a little unclear, but I think if the density of the liquid increases by 1.0% for each 10 degrees Celcius drop in temperature (the inverse of the statement from the problem), then it would increase by 3.0% for a 30 degree drop, and so on. So take the Celcius temperature drop that you calculated, and divide by 10, then multiply by 1.0% to find the percentage increase in density. Then take the percentage increase, add one to it, and multiply by the density at 86 degrees Fahrenheit that you calculated. For example, for a 3.0% increase, your factor is 1.03.