2012/06/27

Coupled heat capacity problem


A 25.78g block of Fe(s) at 47.15℃ is dropped into 100.0g of ethanol at 4.87℃. When the system reached thermal equilibrium, what is the temperature? Assume the system is perfectly insulated/isolated. Heat capacity of Fe(s) = 0.451J/g℃ and of ethanol = 2.46J/g℃.

This is a “coupled systems” problem. The “hot” Fe(s) will lose energy/heat that will be absorbed by the “cold” ethanol. Qualitatively, the final temperature must be less than 47.15℃ and greater than 4.87℃, given the relative amounts and properties of Fe(s) and ethanol, it's reasonable to assume that the final temperature will be closer the 4.87℃ than 47.15℃. Because the system is “perfectly insulated”, all of the energy lost by the Fe(s) will be gained by the ethanol. So the energy picture is:
Eout(from Fe(s)) = (0.451J/g℃)(25.78g)(Tf – 47.15℃)
Ein(to ethanol) = (2.46J/g℃)(100.0g)(Tf – 4.87℃)
Let's look at 2 ways to treat this, one is more rigorously mathematical, the other in still mathematical, but involves a little hand-waving. You can decide which is which...
Using the equations as written above, we have a “frame of reference” problem. Eout should equal Ein, but in order to do the straight-up algebra, we need to approach the problem from a single frame of reference. What does this mean? The short answer? Sneak a little negative sign into the equation. The effect of this will be to change the frame of reference of one of these energies so that they're both the same. Then it's an algebra problem to solve for Tf:
- (0.451J/g℃)(25.78g)(Tf – 47.15℃) = (2.46J/g℃)(100.0g)(Tf – 4.87℃)
For simplicity's sake, I know that all of the units are going to cancel (except for the final ℃), so I'm going to drop them. Let's bunch all of the constants together...
(-0.04726)(Tf – 47.15℃) = (Tf – 4.87℃)
Distributing the constant...
-0.04726Tf + 2.22847 = Tf – 4.87
Grouping “Tf” terms and number terms...
2.22847 + 4.87 = (1 + 0.04726)Tf
7.098 = 1.04726Tf
And the final step gives...
Tf = 6.78℃
If we'd rather treat this as a “magnitude of energy” problem, then we don't have to mess around with adding a negative sign. We can do this by using the absolute value of the change in temperature. Do you have an “absolute value” button on your calculator? I don't think I do... Fortunately, this is a real-world problem, so we can use a little intuition to make thing behave. Since Tf is greater than 4.87, the (Tf – 4.87℃) term will be positive, so the absolute value takes care of itself. The other temperature change, (Tf – 47.15℃), will be negative {since we know that Tf is less than 47.15}, so the absolute value of this term will be... (47.15℃ – Tf). Now we can plug in and once again solve:
(0.451J/g℃)(25.78g)(47.15℃ – Tf) = (2.46J/g℃)(100.0g)(Tf – 4.87℃)
(0.04726)(47.15℃ – Tf) = (Tf – 4.87℃)
2.22847 – 0.04726Tf = Tf – 4.87℃
2.22847 + 4.87 = (1 + 0.04726)Tf
7.098 = 1.04726Tf
Tf = 6.78℃
Same result either way.

2012/06/26

Polyatomic ions

You should know the following polyatomic ions:
Nitrate (NO3-1), sulfate (SO4-2), carbonate (CO3-2), phosphate (PO4-3), chlorate (ClO3-1), bromate (BrO3-1), iodate (IO3-1), hydroxide (OH-1), cyanide (CN-1), cyanate (OCN-1), thiocyanate (SCN-1), thiosulfate (S2O3-2), permanganate (MnO4-1), chromate (CrO4-2), dichromate (Cr2O7-2), ammonium (NH4+1)
Notice that when "thio" appears in the name, it often means that one of the oxygens has been replaced by a sulfur.
In a couple weeks we'll be looking at acids and bases, and a number of these polyatomic ions can be protonated to form additional polyatomic ions that you should also know such as:
bicarbonate/hydrogen carbonate (HCO3-1), bisulfate/hydrogensulfate (HSO4-2), hydrogen phosphate (HPO4-2), dihydrogen phosphate (H2PO4-1)
Oxoanions are systematically named using suffixes and prefixes, so you should be able to determine formulas/names for the full family of an oxoanion. Let's look at the chlorine family as an example... chlorATE is ClO3-1. If we add an oxygen to chlorate but keep the same charge, we get PERchlorATE, ClO4-1. If we remove an oxygen from chlorate but keep the same charge, we get chlorITE, ClO2-1. If we remove another oxygen but keep the same charge, we get HYPOchlorITE, ClO-1. If you know all the "-ate" versions of the oxoanions, you should be able to get the rest of them.


2012/06/24

Welcome to Summer 2012!

Welcome to Gen Chem II (CHEM 210) for Summer 2012. We've got a tight 5-week schedule and a lot of material to cover. I'll try to post blog and/or twitter updates every day, but with the pace of the class I may miss a day or two. Look back over blog posts from January-May 2012 for info. If you're on Twitter, I'll be tweeting about class with #GenChem2012. See you bright and early!