Tutor profile: Andrew H.

Solve for the roots of the equation 2x^2 + 9 = 7x + y

The first step is to move everything over to one side. This get the new equation 2x^2 - 7x + 9 = y. This equation then has y set equal to zero as solving for roots means the x-intercepts which are found when y = 0. There are various methods one can attempt to solve for this such as completing the square, graphing, or solving for the roots by factoring; however, all of these yield no solutions. If one graphs, they will see no x-intercepts, so one must resort to using the quadratic formula and will expect imaginary solutions. This formula is usually given during exams or memorized depending on the teacher or professor or the exam given. Using a = 2, b = -7, and c = 9 the roots are x = (7 - i sqrt(23)) / 4 x = (7 + i sqrt (23)) / 4

Assume a player is working to achieve level 99 in a video game and they are currently half way to level 99. If the total experience the player has doubles every 7 levels, what is there current level?

92

An environmental engineer is using data gathered by a local state park to measure air pollution from summer family barbecues. Before he can use the numbers provided by the park, he needs to know the mass of carbon dioxide emitted from burning an entire propane cylinder. He remembers that burning propane (C3H8) with oxygen (O2), which is assumed to be in excess, produces carbon dioxide (CO2) and water vapor (H2O). From his research, he finds the average propane tank used for grilling purposes is 30L volume at 20 atm of pressure. He assumes the average temperature of the summer cook off is 30 degrees Celsius. Show him the steps to find the mass of the carbon dioxide pollution in grams.

The steps to solve this problem are multiple and addresses many different aspects of a student's ability to solve chemical equations. The general solution pathway is as follows: 1. Solve for the quantity of propane is in the tank (this is done using ideal gas law) that will be reacted 2. Balance the combustion reaction for propane and oxygen yielding water and carbon dioxide 3. Use the quantity of propane reacted found in part one and coefficients of the balanced reaction solved in part 2 to solve for the molar amount of carbon dioxide produced 4. Solve for the molar mass of carbon dioxide to convert molar amount of carbon dioxide produced to mass of carbon dioxide produced Step 1: PV = nRT P= 20 atm, V = 30 L, n = solve for, R = 0.082057 (atm*L)/(K*mol), T = 30C It is important to make sure that the R value chosen matches the units of P, V, and T. In this case, R has temperature units of Kelvin, so the temperature in Celsius must be converted. This R value is typically supplied in a table or memorized prior to an exam depending on professor/teacher. K = C + 273. T is 303K and this will be used for the calculation. Plugging the known variables in solving for n yields 24.13 moles of propane in the tank. Step 2: The generic combustion reaction for propane without coefficients is below. _C3H8 + _O2 ---> _H2O + _CO2 To balance combustion reactions, it is important to balance first for hydrogen and carbon on the RHS first, then balance the LHS with the oxygen need. To balance for the 3 carbons on the RHS, 3 carbons are needed on the LHS and this is achieved with a 3 coefficient for CO2. The same is done for the 8 hydrogens needed on the RHS by putting a 4 coefficient on H2O giving us: 1 C3H8 + _ O2 --> 4H2O + 3CO2 It can be seen from this that 10 oxygen atoms are needed on the LHS to balance the RHS. This is done with a coefficient of 5 on O2 giving a final balanced reaction listed below. 1 C3H8 + 5O2 --> 4H2O + 3CO2 Step 3: It can be seen from the reaction found in part 2 that 3 moles of carbon dioxide are produced for every 1 mole of propane reacted. Therefore, the amount of propane in the tank found in part 1 (in moles) can be converted to carbon dioxide produced by multiplying by this ratio and following the unit cancellation 24.13 mol C3H8 * (3 mole CO2 produced / 1 mole C3H8 reacted) = 72.39 mol CO2 produced Step 4: To convert the amount of molecules (in moles) to a mass of CO2, one must first calculate the molar mass. The molar mass is the ratio of molecules in moles to the mass of the substance. This equation is shown below: Molar Mass of substance (Mm) = moles of substance (mol) / mass of substance (m) Mm = mol/m The molar mass can be found by tabulating the atomic mass of each atom in the chemical formula and these values are found on the periodic table. For CO2, this would be 1 carbon and 2 oxygens. The value for C is approximately 12 and for oxygen approximately 16. This gives a molar mass of 44. Using the answer from part 3 for the moles of CO2, one can algebraically solve for the answer. 44 g CO2/mol CO2 = 72.39 mol of CO2 / m CO2 m = 3185.45 g of CO2.