If there are 17 fruits total in a basket. There are half as many apples as there are bananas and 3 more than twice as many oranges as there are bananas. How many apples, bananas and oranges are there?
1) Start with the fruit with the least number and label it as 'x.' In this case, the apples! 2) Put all fruits in terms of apples (x): Apples = x Banana = 2x Oranges = 2(bananas)+3 = 2(2x) + 3 3) Add all fruits in terms of x adding up to total fruits (17) and solve x. Total fruits = apples + banana + oranges 17 = x + 2x + 2(2x)+ 3 17 = x + 2x + 4x + 3 (*** combine like terms) 17 = 7x + 3 (*** substract 3 from both sides) 14 = 7x (*** divide both sides by 7) 2 = x 4) Using x, determine the number of each fruit. Apples = x = 2 apples Banana = 2x = 2(2) = 4 bananas Oranges = 2(bananas)+3 = 2(2x) + 3 = 2(2*2) + 3 = 2(4) + 3 = 8 + 3 = 11 oranges
Salicylic acid (moalr mass 138g/mol) and acetic anhydride (molar mass 102g/mol) react together in the presence of a strong acid (such as phosphoric acid) to produce acetylsalicylic acid (commonly known as aspirin) and acetate. If 1.5grams of salicylic acid and 3ml of acetic anhydride are added to a flask for this reaction, what is the theoretical yield of acetylsalicylic acid (molar mass 180g/mol)? (density of Acetic Anhydride is 1.08g/ml)
Salicylic Acid = SA; Acetic Anhydride = AA; Acetylsalicylic acid - ASA; acetate = A 1) List the known variables and determine what information is missing. Known = SA grams & molar mass; AA ml (vol), density & molar mass Unknown = grams ASA 2) Find the limiting reagent by determining which reactant contains the least number of moles. The moles of limiting reagent is equivalent to the moles of the product (given that the molar ratio of is 1:1). To calculate moles, use the formula Molar Mass= g/mol so moles = g/(Molar Mass). In other words, simply try to mathematically cancel the units so that the desired unit remains: Moles SA = (grams SA) * (1/molar mass SA) (1.5g)*(1/138g/mol) = 0.011moles SA Moles AA = (density of AA) * (ml AA) * (1/molar mass AA) (1.08g/ml)*(3ml)*(1/102g/mol) = 0.032 moles AA SA contains less moles than AA, SA (Salicylic Acid) is the limiting reagent. 3) Determine the theoretical yield (grams) ASA using the moles of limiting reagent. (Limiting reagent (SA) moles) * (molar ratio of ASA to SA) * (molar mass of ASA) = grams ASA (0.011moles SA) * (1mol ASA/1molSA) * (180g/mol ASA) = 1.98 grams Acetylsalicylic Acid (ASA)
The breakdown of glucose in the presence of oxygen provides energy needed for the cells. When glucose (C6H12O6) reacts with oxygen (O2), carbon dioxide (CO2) and water (H2O) are produced. What does the balance equation of this reaction look like?
1) As with any balancing equation question, start with the basic reaction that you are given and write it down. Then determine the number of each element in the reactant side and the product side. C6H12O6 + O2 ---> CO2 + H2O Reactant: C (6); H (12); O (8) Product: C (1); H (2); O (3) 2) Balance equation by multiplying molecules on either the reactant or product side until they are equal. It helps to start with whatever has the lowest number and only appears once. For example, start with balancing carbons and hydrogens by multiplying CO2 and H2O by 6. Check the number of all elements again. C6H12O6 + O2 ---> 6 CO2 + 6 H2O Reactant: C (6); H (12); O (8) Product: C (6); H (12); O (18) 3) Balance the remaining elements. Oxygen is the only element that is not balanced and is in greater numbers on the product side. Since O2 is on the reactant side and increasing it only increases the number of oxygen without affecting H or C, O2 needs to be multiplied by 6 to give rise to a total of 18 oxygens. State the final balanced equation and check the numbers one more time. C6H12O6 + 6 O2 ---> 6 CO2 + 6 H2O Reactant: C (6); H (12); O (18) Product: C (6); H (12); O (18)