# Tutor profile: Kristen D.

## Questions

### Subject: Chemistry

How many atoms of oxygen are in a 0.0577 mol sample of nitric acid, $$HNO_{3}$$?

First things first, it's imperative that we recognize the type of problem here. This is an example of a dimensional analysis problem, where one unit is converted to another. It's a good resource to find out the relationship among different quantities and is very useful when working in the lab. In this case, we are using moles (SI unit to measure the amount of a substance) to figure out how many atoms are needed. Dimensional analysis involves using the factor-label method, which is a problem solving method that helps keep your work organized. Let's reread the question and identify what information is given and what is being asked. We are clearly given the amount of moles in the $$HNO_{3}$$ sample, which is 0.0577, and we want to know many atoms are present within that sample. So again, the goal is to convert from moles to atoms! In these type of problems, we ALWAYS start with our given, which is 0.0577 mol. Factor labeling involves setting up different conversion factors as fractions, getting diagonally aligned units to cancel out, so we can get to our final destination, atoms. Anyways, let's take our 0.0577 mol and put it over one (this step isn't mandatory and can leave the given as is; however, I find the fractions easier to see when the given is also written as a fraction, putting it over one). Let's figure out what our conversion factor will be. Since we're working with moles, it would make sense to use a conversion factor involving moles, to get the unit to cancel out. In order to completely move on from moles and work in terms of atoms, we need to identify a mole-to-mole ratio, which is an in-between point to convert between moles of two substances. Notice how our given is in terms of $$HNO_{3}$$ and the answer calls for atoms of oxygen. We must use the mole-to-mole ratio to go from moles of $$HNO_{3}$$ (given) to moles of oxygen. Looking at the formula, $$HNO_{3}$$, what do you notice about the oxygen? It appears to have a subscript of 3, which tells us that for every mole of $$HNO_{3}$$, we have 3 moles of oxygen. That is our conversion factor! We can write it next to our given as 3 moles of oxygen over 1 mole of $$HNO_{3}$$. We now have two fractions in our conversion: our given over one and our mole-to-mole ratio. Since units cancel out diagonally, our moles of $$HNO_{3}$$ are completely cancelled out, leaving us with moles of oxygen. We are almost there! Now we must go from moles of oxygen to our final destination, atoms of oxygen. This conversion factor will involve what we call Avogadro's number, which is a set, absolute number that tells us how many atoms are present in a mole of a particular substance. This is a universal number of $$6.022 x 10^{23}$$ that can be applied to any substance! It is a constant, so it stays the same, no matter what the problem is, and it's always written per mole of a substance. Moving on, since our previous conversion factor has moles of oxygen in the numerator, we must put moles of oxygen in the denominator of this current conversion, so that moles of oxygen cancel out. We can put $$6.022 x 10^{23}$$ atoms of oxygen over 1 mole of oxygen. The moles of oxygen cross out and we're left with atoms of oxygen, which is what the problem asked for. We no longer need to keep going with the factor labeling. Instead, we can multiple our fractions together to get a numerical answer. Multiplying the three numerators across, we get a final answer of $$1.04 x 10^{23}$$ atoms of oxygen (notice how the answer is written in scientific notation and is rounded to the correct number of significant figures, which is 3, since our given contains 3 sig figs). To summarize everything above using math, we get the following: $$\frac{0.0577molHNO_{3}}{1} \times \frac{3molO}{1molHNO_{3}} \times \frac{6.022\times10^{23}atomsO}{1molO} = 1.04 x 10^{23} atomsO$$

### Subject: Basic Chemistry

Classify the compound magnesium hydroxide as ionic or covalent. Then, write the formula for the compound.

First, let's review what it means for a compound to be ionic or covalent. An ionic compound is an electrically neutral compound (overall/net charge of 0) that consists of a cation, or positive ion (usually metal elements that lost electrons, resulting in a positive charge) and an anion, or negative ion (usually nonmetal elements that gained electrons, resulting in a negative charge). Ionic compounds contain ions that will gain or lose electrons, resulting in electrons being transferred/donated, not shared. As for covalent compounds, these typically include nonmetal elements or elements of similar nature (such as two polyatomic ions), involving the sharing of electron pairs, unlike ionic compounds. That being said, let's further analyze magnesium hydroxide. According to the periodic table, magnesium is found in group 2A, the alkaline earth metals, meaning that it must have metallic properties, hence it is a metal. This only tackles the first half of the compound- we still need to analyze hydroxide. Notice how hydroxide has an -ide ending. Whenever we see -ide, that means we're working with an ion (something with a charge). In the case of hydroxide, it is a polyatomic ion, meaning it's a set of two or more atoms covalently bonded together that behave as a single unit with charge. Just because we have a polyatomic ion in our compound, doesn't necessarily mean that the overall compound will be covalent though, even though covalent bonds are present within the polyatomic ion. Again, keep in mind that all polyatomic ions function as a single unit! Anyways, it's best to identify polyatomic ions using a reference table or chart with the most common ones listed (a lot of high school and college chemistry courses will provide these materials to students and in some cases, expect students to memorize them). Hydroxide is almost always listed as a common polyatomic ion, so it's safe to say we can classify it as one. A reference table shows that hydroxide has a negative charge. Looking at the compound as a whole, we have a metal (with a positive charge) bonded to a polyatomic ion (with a negative charge), so we classify it as an ionic compound, due to the opposing charges. The difference in charges will result in an electron transfer, hence forming an ionic bond. Now that we've classified the compound as ionic, we can write the appropriate formula. When it comes to writing the formula for ionic compounds, we always start with the cation/metal first, which is magnesium. We need to find its symbol and charge. According to the periodic table, magnesium is abbreviated as Mg and has a +2 charge (many courses require students to memorize element symbols, making this process a lot quicker and easier). As for hydroxide, we need to look at a reference table to see its symbol and charge. According to a polyatomic ion table, hydroxide is abbreviated as OH and contains a -1 charge (again, it helps to memorize this). Combining the two, we get: $$Mg^{+2}OH^{-1}$$. It would be great if we could stop here and leave it as $$Mg^{+2}OH^{-1}$$; however, notice the charges. Like I said above, an ionic compound is an electrically NEUTRAL compound, with a net charge of 0. $$Mg^{+2}OH^{-1}$$ is not electrically neutral, since the +2 and -1 charges don't cancel each other out. Think of it almost as an algebraic expression, where each ion has its own, separate side to the equation: 2 = -1x. What can we do to the OH charge (-1x), so that it will balance out the Mg charge (2)? If we divide both sides by -1, we're left with x = -2. So, OH must have a net charge of -2 to cancel out with the Mg, so we can put a subscript of 2 next to the OH, since 2 multiplied by its charge of -1 will cancel out the +2 in Mg. In our final answer, OH should have parentheses around it because this will help show that it's a polyatomic ion, instead of it being two separate elements of O and H. Our final answer would be the following: $$Mg(OH)_{2}$$

### Subject: Algebra

Solve for x: $$3(x+6)-4(3x-2) = -10$$

When I first look at this problem, I notice that there are parentheses with numbers on the outside. These parentheses mean that we must apply the distributive property, since our equation contains an expression in the form of $$a(b+c)$$. In general, to distribute means to dispense or deliver something, so we are going to deliver the number outside the parentheses to each separate item inside the parentheses through multiplication. Let's apply the distributive property to our above equation, one expression at a time, starting with $$3(x+6)$$. Imagine 3 is a mailman and needs to deliver packages to two houses: x and 6. The first house he comes across is x. Once the mailman (3) delivers the package to the first house (x), we can then deliver the 3 to the x by multiplying them together, getting 3x. Now the mailman (3) can move onto his next house, which is 6. After the second package is successfully delivered, we deliver the 3 to the 6, multiplying them together to get 18. As a result of this expression, we get $$3x+18$$ (the addition sign comes from 18 being a positive number). Moving onto our second expression, $$-4(3x-2)$$, let's apply the same concept. In this case, the -4 is our mailman and needs to deliver packages to houses 3x and -2. After delivering a package to our first house, 3x, the -4 can be delivered to the 3x, multiplying them together to get -12x (remember, a positive multiplied by a negative will give you a negative answer). The mailman (-4) moves onto the second house, -2, to deliver its package, meaning we can deliver the -4 to the -2, multiplying them together to get 8 as a result (remember, a negative multiplied by a negative will give you a positive answer). As a result of this expression, we get $$-12x+8$$ (the plus comes from 8 being positive). We now have evaluated everything on the left side of the equation, so combining our two expressions, we are left with $$3x+18-12x+8 = -10$$. We are not quite done yet. Do you notice how there are like terms, terms that have the same variables and powers, on the left side of our equation? For example, 3x and -12x are like terms because they both contain an x raised to the same power of 1 (we assume it's 1, since there are no exponents written in). Also, 18 and 8 are like terms, as they are both constants, or just plain old numbers on their own. That being said, let's combine these like terms to simplify our equation (we always want to simplify in algebra as much as possible before solving). Adding 3x and -12x, we get -9x, and adding 18 and 8, we get 26. So now, the equation looks like this: $$-9x+26 = -10$$. This looks more solvable now, compared to all of those parentheses in the beginning! Our goal now is to solve for x, meaning we want x by itself. To do that, we must get rid of the 26 by performing the opposite operation, which in this case is subtraction (subtraction is the opposite of addition). What we do to one side, we must do to the other, so let's subtract 26 from both sides. This completely eliminates 26 from the left, ending up with -10-26 on the right. Simplifying the right side, we get -36. We now have the following equation: $$-9x = -36$$. We still don't have x completely by itself since there is a -9 in front of it. We must reverse this to get rid of the 9 on the left, which means we will divide both sides by -9 (division is the opposite/reverse of multiplication). The x is by itself now on the left and on the right, we have -36/-9, which can be simplified to 4. Finally, we can conclude that our solution is $$x = 4$$. To double check our work, we can go back into the original equation given to us and plug in 4 wherever there's an x. Substituting the four in, we get: $$3(4+6)-4(34-2) = -10$$. This can be solved using the order of operations (PEMDAS- "Please Excuse My Dear Aunt Sally"). All this means is that we complete the mathematical operations in a specific order, starting with parentheses, exponents, multiplication/division, and addition/subtraction. According to this, let's start with the parentheses, solving everything inside them. We then get $$3(10)-4(12-2)$$. Notice how in the second parentheses, I multiplied the 3 and 4, instead of subtracting 2 from 4, since multiplication comes before subtraction in PEMDAS. Anyways, simplifying that further, we get $$3(10)-4(10) = -10$$. We can multiply 3 and 10 and -4 and 10 to get $$30-40 = -10$$. We end up with $$-10 = -10$$. When both sides equal each other, it means that we solved for x correctly, so we are 100% certain that $$x = 4$$. Whenever you have enough time on a quiz or exam, it's important to use this checking method to ensure your math is correct. In these types of problems, math errors are very common, so it's good to go the extra mile and check your answer using this method!

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