Tutor profile: Jordyn M.
0.018 g of pure hydrochloric acid is mixed into 500. mL of water. Assume the volume change upon the addition of hydrochloric acid is negligible. (A) What is the molarity of this solution? (B) What is the pH of the resulting solution?
(A) The molarity of a solution is moles of solute divided by liters of solution. The first step is to determine the moles of hydrochloric acid that were added. The formula for hydrochloric acid is HCl, and we need to find its molar mass. The molar mass of hydrogen is 1.01 g/mol, and the molar mass of chlorine is 35.45 g/mol. We can find these values on the periodic table. Since HCl has a 1:1 ratio of hydrogen:chlorine, we add the molar masses of the constitutive elements. The molar mass of HCl is: 1.01 g/mol + 35.45 g/mol = 36.46 g/mol Then, we need to convert grams to moles. The problem states we have added 0.018 g HCl. To convert this to moles, we use the 36.46 g/mol molar mass we just found. We need to multiply in a way that cancels out grams to give us moles. (0.018 g HCl)*(1 mol HCl/36.46 g HCl) = 0.00049 moles HCl Then, we need to divide moles of solute by liters of solution. 500 mL is equal to 0.500 L. Molarity of solution = 0.00049 moles HCl / 0.500 L solution = 0.00098 M HCl Our answer for (A) is thus 0.00098 M HCl. Sig figs are important! Since 0.018 g has 2 sig figs and 500. mL has 3 sig figs, our answer should have the lowest number of sig figs given by the problem. Thus, our answer has 2 sig figs. (B) To determine the pH of the solution, we use the equation pH = -log[H+] We need to determine the concentration of H+ ions in solution. Since HCl is a strong acid, it dissociates fully in solution into H+ ions and Cl- ions. The concentration of HCl is 0.00098 M, as we determined in part (A). This is the concentration of the molecule as a whole, but it is also the concentration of H+ ions in solution. Each molecule of HCl dissociates into one H+ ion and one Cl- ion. We can do the math to make sure by considering the proportion of H+ in the molecule: 0.00098 M HCl = (0.00098 moles HCl/ 1 L solution)*(1 mol H+/1 mol HCl) = 0.00098 moles H+/1 L solution = 0.00098 M H+ Then, we can plug the concentration of H+ ions into the pH equation: pH = -log(0.00098 M H+) = 3.00 Our answer is thus pH 3.00. *Note: When dealing with pH values, only the digits after the decimal point are significant. So, pH 3.00 only has 2 sig figs, which is what we want given the problem.
Subject: Basic Chemistry
An atom has 18 neutrons, 18 electrons, and an overall charge of -1. (A) How many protons are present in this atom? (B) What is the atomic number? (C) What element is this? (D) What is its mass number?
(A) We can find the number of protons by considering the overall charge and the number of electrons. Each electron has a charge of -1, and each proton has a charge of +1. In a neutral atom, the number of electrons equals the number of protons. In order for the atom to have an overall charge of -1, there needs to be one more electron than protons. Therefore, there are 17 protons in this atom. (B) The atomic number is the number of protons in the nucleus of an atom. We determined this to be 17 protons in part (A). Therefore, the atomic number is 17. (C) Each element has a unique atomic number. As explained in part (B), the atomic number is 17. Looking at a periodic table, the element with atomic number 17 is chlorine. (D) The mass number is the number of neutrons plus the number of protons, since each proton and each neutron is 1 atomic mass unit. Electrons are so small compared to neutrons and protons that their mass is ignored. 18 neutrons + 17 protons = 35. Therefore, the mass number is 35.
At a bookstore, Jordyn purchased several books and several magazines. Each book costs $5, and each magazine costs $2. She spent $40 and purchased 11 items in total. (A) How many books and how many magazines did she buy? (B) The next time she visits the store, there is a sale going on, and she will receive 10% off her purchase. If her purchase comes to $20 with the sale, how much would she have spent without the sale?
(A) We need to set up a series of equations to solve this problem. We have two variables to find (the number of books and the number of magazines), and so we need to create 2 equations. Let's first define our variables: b = number of books bought. m = number of magazines bought. We know that she bought 11 items in total. Therefore, b + m = 11. We also know the cost of each item and how much she paid for everything. To figure out how much she paid for books, we multiply the number of books by the cost of each book. To figure out how much she paid for magazines, we multiply the number of magazines by the cost of each magazine. We then add these numbers, and they must sum to $40 in total. Therefore, 5b + 2m = 40. We then need to combine these equations so we can figure out what b and m are individually. It is easiest to use the first equation to solve for one of the variables. Let's solve for b (but you would get the same answer by solving for m! Try it). b + m = 11 Subtract m from each side. b + m - m = 11 - m The m variables on the left side of the equation cancel out, giving us: b = 11 - m We can then plug in what we've solved for b into the second equation we created. 5b + 2m = 40 5(11 - m) + 2m = 40 Then, you need to use your knowledge of PEMDAS to solve for m. First, we distribute by multiplying the 5 by each value in the parentheses: 55 - 5m + 2m = 40 Then, we can add the two terms that contain m. (Remember the negative sign in front of the 5m: -5 + 2 is the same as 2 - 5) 55 - 3m = 40. Then, subtract 55 from each side. 55 - 3m - 55 = 40 - 55 -3m = -15 Then, divide each side by -3. Remember, dividing a negative number by a negative number makes the solution positive. (-3m/-3) = (-15/-3) m = 5 We found the number of magazines she purchased! Now, we can use the number of magazines to find the number of books. It will be easiest to do this with the first equation that we rearranged: b = 11 - m b = 11 - 5 b = 6 She purchased 5 magazines and 6 books. (B) This question requires some thinking. If there is a 10% off sale, that means she paid 90% of what she would have paid without the sale. She paid $20 with the sale. So, $20 is 90% of what she would have paid without the sale. We need to find the cost without the sale. Let's say x = cost without the sale. 90% as a decimal is 0.90. We paid 90% of what we would have paid without the sale, so we paid 0.90x. We know we actually paid $20 with the sale. Therefore, 0.90x = 20 Divide both sides by 0.90. (0.90x/0.90) = (20/0.90) x = $22.22 Thus, without the sale, she would have paid $22.22. We can check this by taking 10% off $22.22. Remember, 10% as a decimal is 0.10. (0.10)*(22.22) = $2.22 Since 10% of $22.22 is $2.22, she paid $2.22 less with the sale. Let's subtract that from the cost without the sale and see if we get what she paid with the sale. $22.22 - $2.22 = $20 This is what she paid with the sale, so we know our work is right!
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