# Tutor profile: Jacqueline B.

## Questions

### Subject: Chemistry

How much energy is produced in the complete combustion of propane in the reaction $$C_{3}H_{8} (g)$$ + $$O_{2} (g)$$ $$\rightarrow$$ $$CO_{2} (g)$$ + $$H_{2}O (l)$$. The enthalpy of formations of propane, carbon dioxide, and water are, respectively, -104 J/mol, -393 J/mol, and -286 J/mol.

The first step is to make sure the reaction is balanced. It isn't in this case, so we need to balance the reaction. Let's do it element by element. $$C_{3}H_{8} (g)$$ + $$O_{2} (g)$$ $$\rightarrow$$ $$CO_{2} (g)$$ + $$H_{2}O (l)$$ Because there are 3 carbon atoms entering the reaction as reactants, there must be 3 carbon atoms leaving the reaction as products. Carbon dioxide is the only product that contains carbon, so this is where the three carbons must exit. $$C_{3}H_{8} (g)$$ + $$O_{2} (g)$$ $$\rightarrow$$ $$3CO_{2} (g)$$ + $$H_{2}O (l)$$ Next, we should balance the hydrogens. Propane contributes 8 hydrogens to the reaction, but only 2 go into each water molecule. $$C_{3}H_{8} (g)$$ + $$O_{2} (g)$$ $$\rightarrow$$ $$3CO_{2} (g)$$ + $$4H_{2}O (l)$$ Now we have 3 carbon atoms and 8 hydrogen atoms on both the left and right sides of the equations. The only thing left to balance is the oxygen. There are 10 atoms on the right but only 2 on the left. $$C_{3}H_{8} (g)$$ + $$5O_{2} (g)$$ $$\rightarrow$$ $$3CO_{2} (g)$$ + $$4H_{2}O (l)$$ This is the final balanced equation. The second step is to balance the formation equations. $$3C (s)$$ + $$4H_{2} (g)$$ $$\rightarrow$$ + $$C_{3}H_{8} (g)$$, $$\Delta H_{f} = -104 J/mol $$ $$C_{3}H_{8}$$ $$formed$$ $$C (s)$$ + $$O_{2} (g)$$ $$\rightarrow$$ + $$CO_{2} (g)$$, $$\Delta H_{f} = -394 J/mol $$ $$CO_{2}$$ $$formed$$ $$H_{2} (g)$$ + $$\frac{1}{2}O_{2} (g)$$ $$\rightarrow$$ + $$H_{2}O (l)$$, $$\Delta H_{f} = -286 J/mol $$ $$H_{2}O$$ $$formed$$ Because enthalpy is a state function, we can add a combination of the enthalpies of formation together to calculate the overall heat of combustion. This means we will be "adding" reactions as well. First, let's reverse the formation of propane reaction because it's used as a reactant during combustion. This means we also have to flip the sign of its enthalpy. $$C_{3}H_{8} (g)$$ $$\rightarrow$$ + $$3C (s)$$ + $$4H_{2} (g)$$, $$\Delta H_{f} = 104 J/mol $$ $$C_{3}H_{8}$$ $$destroyed$$ Then there are 3 moles of carbon dioxide to consider. This means we also have to multiply everything, including its enthalpy, by 3. $$3C (s)$$ + $$3O_{2} (g)$$ $$\rightarrow$$ + $$3CO_{2} (g)$$, $$\Delta H_{f} = -1182 J/mol $$ $$3CO_{2}$$ $$formed$$ And then we must manipulate the water equation to use 5 total moles of oxygen gas. Don't forget that we already have 3 moles from the carbon dioxide equation $$4H_{2} (g)$$ + $$2O_{2} (g)$$ $$\rightarrow$$ + $$4H_{2}O (l)$$, $$\Delta H_{f} = -1144 J/mol $$ $$4H_{2}O$$ $$formed$$ If we add these three equations together, we get: $$C_{3}H_{8} (g)$$ + $$3C (s)$$ + $$3O_{2} (g)$$ + $$4H_{2} (g)$$ + $$2O_{2} (g)$$ $$\rightarrow$$ + $$3C (s)$$ + $$4H_{2} (g)$$ + $$3CO_{2} (g)$$ + $$4H_{2}O (l)$$ And if we combine terms and eliminate what exists on both sides of the reaction, we get: $$C_{3}H_{8} (g)$$ + $$5O_{2} (g)$$ $$\rightarrow$$ + $$3CO_{2} (g)$$ + $$4H_{2}O (l)$$ Enthalpy-wise, this is $$\Delta H_{f} = 104 J/mol $$ $$C_{3}H_{8}$$ $$destroyed$$ + $$\Delta H_{f} = -1182 J/mol $$ $$3CO_{2}$$ $$formed$$ + $$\Delta H_{f} = -1144 J/mol $$ $$4H_{2}O$$ $$formed$$ And so, we get $$\Delta H_{combustion}=-2222 J/mol$$ $$C_{3}H_{8}$$ $$destroyed$$

### Subject: English

Which stylistic device is used in the sentence "Peter Piper picked a peck of pickled peppers"? a) onomatopoeia b) alliteration c) irony d) metaphor

The answer is "alliteration". Alliteration is a device whereby neighboring words in a phrase share the same initial consonant sound. In this case, that sound is "p". An "onomatopoeia" is a word whose pronunciation reflects a sound. A "metaphor" is a figurative comparison made without the use of the words "like" or "as". While "irony" can refer to three different concepts, in the verbal sense it is the use of words to convey a meaning different from the literal. Neither "dramatic irony" nor "situational irony" fit the sentence provided.

### Subject: Algebra

Gemini has just graduated school and is ready to start working. An intense job search leaves two offers to consider. Company A promises a pay of $1500 per week and a yearly bonus of $3500, while Company B offers $1400 per week and a yearly bonus of $10000. Which offer is best if Gemini wants to earn the largest amount of money possible in five years? Assume Gemini works 47 weeks a year.

First, rewrite the given information into a $$y=mx+b$$ format and use dimensional analysis to make sure things are in the right place: $$1500x \frac{dollars}{week} + \frac{3500 \frac{dollars}{year}}{\frac{47}{1} \frac{weeks}{year}}$$ $$1400x \frac{dollars}{week} + \frac{10000 \frac{dollars}{year}}{\frac{47}{1} \frac{weeks}{year}}$$ Because the question mentions "years", it's good to keep everything in units of $$\frac{dollars}{year}$$: $$1500x \frac{dollars}{week} * 47 \frac{weeks}{year} + 3500 \frac{dollars}{year}$$ $$1400x \frac{dollars}{hour} * 47 \frac{weeks}{year} + 10000 \frac{dollars}{year}$$ If you plug $$x = 1$$ into the equation, you will find that Gemini can make $$$74000$$ after one year with Company A and $$$75800$$ after one year with Company B. But because the slope ($$m$$ in $$mx$$) of the first equation is greater, you know that the salary for Company A will eventually overtake that of Company B. The problem asks if that takeover occurs in the first five years. Now you can solve the problem in at least two different ways: $$1)$$You could set the two equations equal and solve for $$x$$. If $$x > 5$$, Gemini should take the offer from the Company B because their salary would still be higher than Company A's at that point. If $$x < 5$$, Gemini should take the offer from Company A because the intersection would have already occurred by the 5-year mark. In this case, you should get $$x = 1.383$$ years. $$2)$$You can plug $$x = 5$$ into both equations and compare the amount of money earned. For Company A, this is $$$356000$$, and for Company B this is $$$339000$$. Therefore, Gemini should take the offer from $$Company$$ $$A$$.

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