# Tutor profile: Tiffany T.

## Questions

### Subject: Chemistry

What charge or oxidation number should be assigned to the polyatomic ion, SO4?

We can refer to the oxidation numbers of each individual atom in the polyatomic ion by looking at the periodic table. We note that S, sulfur, is in the column that can have an oxidation number of either -2 or +6. Since it is outnumbered by oxygen here, we assume that it takes on the +6 charge. Oxygen is in the same column, and has an oxidation number of -2. We can sum these oxidation numbers to get the total charge for SO4: +6 + 4(-2) = -2, so SO4 should have a charge of -2.

### Subject: Basic Chemistry

One basic chemical reaction is CH4 + O2 --> H2O + CO2. Assuming we start off with 6 grams of CH4, how many grams of CO2 will we end up with if the reaction completely follows through?

This is a stoichiometry question! In order to solve for the grams of CO2 that will be produced from the reaction, we need to first know how many moles of CH4 is equivalent to the grams we are starting off with. It is important to remember that a reaction dictates the relationships of the number moles of each molecule. To convert from grams to moles, we need to know the molar mass of CH4. To compute the molar mass of CH4, we can refer to a periodic table for the atomic weights of C, carbon, and H, hydrogen. The molar mass will be the sum of one carbon atom's weight and 4 hydrogen atom's weights: 12.01 grams (carbon) + 4(1.008) grams (hydrogen) = 16.04 grams CH4/mole CH4 Recall that the molar mass tells us how many grams there are of a substance per mole! Given this we can now convert the 6 grams of CH4 we have initially to how many moles we have of CH4: 6 grams CH4 * (moles CH4/16.04 grams CH4) = 0.374 moles of CH4 (Note that the grams of CH4 on the top and bottom of this expression cancel out!) From here we can use the reaction given to see how many moles of CO2 are produced per moles of CH4! As we can see from the reaction, one mole of CH4 produces one mole of CO2. From this relationship, we therefore know that 0.374 moles of CH4 produces 0.374 moles of CO2. We need to convert moles of CO2 now to grams of CO2! We can do this by doing the reverse of what we did for CH4. Let's find the molar mass of CO2, which has one carbon atom and two oxygen atoms. 12.01 grams (carbon) + 2 (16.00) grams (oxygen) = 44.01 grams CO2 /mole CO2 With this relationship, we can now convert 0.347 moles of CO2 we know are produced to grams of CO2: 0.347 moles CO2 * (44.01 grams CO2/ mole CO2) = 15.3 grams CO2 produced from 6 grams of CH4!

### Subject: Algebra

My father’s age divided by 5 is equal to my brother’s age divided by 3. My brother is 3 years older than me. My father’s age is 3 less than 2 times my age. How old is my father?

To first solve this question, we need to assign variables to the unknowns! The unknowns in this question are X, the father's age, Y, the brother's age, and Z, my age in years. We can create equations that help make connections between each of these variables. First, the father's age and the brother's age: X/5 (the father's age divided by 5) = Y/3 (is equal to the brother's age divided by 3) Then, the relationship between the brother and me! Y = Z + 3 (my brother is 3 years older than me) Lastly, the father's age compared to my age: X = 2Z - 3 (3 less than two times my age) Given these relationships, we can solve for each variable. If we solve for Z, we can find the rest of the variable values. In order to this, we need to simplify the three equations down to just two equations with two variables that can be solved. Let's replace Y in the second equation with X. To do this we can use the first relationship to substitute for Y. With some rearranging and cross multiplying of the first equation, we see that Y = (3/5)X. Now that we know this, we can substitute Y in Y = Z+3, the second equation, with (3/5)X to get two equations and only two unknowns! The two equations we have are: (3/5) X = Z + 3 X = 2Z - 3 Given these equations, we can divide the first equation by 3/5 to isolate just X on the left hand side. When we divide by 3/5s, we get that X = (5/3)Z + 5. Now that we have two equations with X on the left hand side, we can set them equal to solve for Z, my age. (5/3)Z + 5 = X = 2Z - 3 We rearrange this so that the variable Z is on the left and values are on the right. (5/3)Z - 2Z = - 3 - 5 - (1/3) Z = - 8 Z = 24 Now we know that the speaker is 24 years old, and the father's age can be solved through the third equation, the relationship between the speaker and the father. X (the father's age) = 24 * 2 - 3 = 48 - 3 = 45 years old.

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