# Tutor profile: Rachel E.

## Questions

### Subject: Chemistry

A compound containing boron and hydrogen was determined to contain 81.10% boron by mass. What is the empirical formula?

First, let's imagine that we have 100g of this compound. If we had 100g, we would have 81.10g of boron (81.10%) and 18.90g of hydrogen (100-81.10%= 18.90%). We find, using the periodic table, that boron has a molar mass of 10.81g/mol. Hydrogen has a molar mass of 1.01g/mol. Now, we need to find out how many moles of boron we have, and how many moles of hydrogen. If we have 81.10g of boron, and it's 10.81g/mol, then we have 81.10g B / 10.81 g/mol B = 7.502 mol B If we have 18.90g of hydrogen, and it's 1.01g/mol, then we have 18.90g H/ 1.01 g/mol H = 18.75 mol H. Now, we now that our empirical formula is going to have whole numbers for both boron and hydrogen. That means that there is going to be a whole number ratio of moles of boron to moles of hydrogen. We start with the ratio 18.75 mol H : 7.502 mol B. Let's now divide by the smallest number: 7.502 Now we have the ratio: 2.5 mol H : 1 mol B Since we need whole numbers for both and not decimals like 2.5, let's multiply the ratio by the lowest whole number that will give the ratio all whole numbers: 2 so 2.5 : 1 times 2 is *5 mol H : 2mol B* This means that our empirical formula has 5 hydrogen atoms for every 2 boron atoms. That means our empirical formula must be: B2H5

### Subject: Biology

Describe the reason behind the structure and formation of cellular membranes.

When we think about cell membranes, we have to think about the individual pieces that make them up. Another name for a cell membrane is a phospholipid bilayer. What does this mean? It means that the membrane is made up of *two layers* of molecules called *phospholipids*. What is a phospholipid? It's a molecule that has a structure that looks kind of like a lollipop: O--- (Imagine this vertically) In this molecule, the O is the phosphate head and the --- is the lipid tail. Why is this important? Well, phosphate, or PO4 3-, has a negative charge (-3). This means that its electrons are not evenly distributed. It's called a "polar" molecule. Lipid molecules, which are made up of a bunch of carbon and hydrogen molecules in a chain, don't have any sort of charge at all. In fact, all of their electrons are pretty evenly distributed. They're what we call "nonpolar". When we put a bunch of these phospholipids in water, something interesting happens. Because one side of the lollipop is polar, and the other is nonpolar, the molecule interacts with water in a really cool way. Water, being composed of an oxygen and 2 hydrogens, is a polar molecule. Most of its electrons tend to hang around the oxygen instead of the hydrogens, so its electrons are not evenly distributed. Polar molecules prefer to be close to other polar molecules, and nonpolar molecules would really rather not interact at all with polar molecules. Because of this, when you put a bunch of phospholipids in water, the phospholipids will arrange themselves so that the phosphate heads are touching water, and the lipid tails are only touching each other. It ends up looking like this: O--- ---O Water O--- ---O Water-based Cytoplasm (Outside) O--- ---O (Inside Cell) O--- ---O See how they arranged themselves into a two-layered membrane? This happened just because of how each end of the molecule interacts with water! This is how all of our membranes are formed.

### Subject: Algebra

Expand (4+3i)(3-2i)

Begin by using FOIL (First, Outer, Inner, Last) First: 4 x 3 = 12 Outer: 4 x -2i = -8i Inner: 3i x 3 = 9i Last: 3i x -2i = -6i^2 (i-squared) Write out: 12-8i+9i-6i^2 Simplify: 12 + i - 6i^2 Remember that i^2= -1 Replace i^2 with -1: 12+i-6(-1) Simplify: 12+i+6 Simplify: 18+i That's your answer!: 18+i

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