Determine the ammonium ion concentration of a solution that results when 4.53 g of (NH4)2SO4 (Molar mass = 132 g/mol) is dissolved in water and diluted to exactly 100.0 mL.
Let's take this problem step-by-step. First, we need to convert the grams of ammonium sulfate ((NH4)2SO4) to moles, for which we need the molar mass, which is given. To find the moles, use the molar mass as a conversion factor. In order to get the number of moles from the mass, you must DIVIDE the mass by the molar mass, which is the same as multiplying by the inverse: [ 4.53 g x (mol/132 g) ]. This way, the unit of mol flips up to the numerator, and the units of grams cancel, leaving you with units of mol, as you are asked to find. The answer to this step is 0.034318 mol of ammonium sulfate (a word about significant figures: while your final answer should be reported to 3 sig figs only, you should always include more sig figs in your calculations in order to avoid errors from rounding too soon, which may be significant). It's a good idea to reread the problem after every step, to make sure you have answered the question or to see the next stepp you need to take. You now have the moles of ammonium sulfate, but the problem asks about ammonium ion. Look at the subscript after the pranthesis around the ammonium ion in the formula: The subscript of 2 means that when ammonium sulfate dissolves, you get 2 moles of ammonium ion for every 1 mole of ammonium sulfate. Therefore, the number of moles of ammonium ion is 2(0.034318), or 0.068636 mol. You are asked for concentration, which means molarity unless otherwise stated. Your answer should be in units of moles ammonium ion/ liter of solution. You have dissolved 4.53 g of ammonium sulfate, which contains 0.068636 mol of ammonium ion, to make a total of 100 mL of solution. Converting mL to L, you get 0.100 L of solution. To get molarity, you perform the division of given mol/L: 0.068636 mol ammonium ion/0.100 L solution gives 0.68636 M of NH4+ ions. Pay attention to sig figs at this point. Your original data contained 3 sig figs, so your final answer should be limited to 3 sig figs as well. You should always include units in your final answer, so you should report your answer as "0.686 M NH4+ ions". Finally, does your answer make sense? The final answer falls within the range of most molarities you have seen so far, so you can have a degree of confidence that you have performed the calculations correctly.
How many moles are in 1.25 grams of sodium chloride, NaCl?
Whenever you see a problem involving both grams and moles, think "molecular weight" or "molar mass" - two different names for the same quantity. To find this value, look up the molar mass for each element in the formula on the periodic table. Sodium (Na) has a molar mass of 22.99 g/mol. Chlorine has a molar mass of 35.45 g/mol. There is one of each type of element in the formula, so add those two numbers together. The molar mass of NaCl is 58.44 g/mol. You are given the mass of sodium chloride. To find the moles, use the molar mass as a conversion factor. In order to get the number of moles from the mass, you must DIVIDE the mass by the molar mass, which is the same as multiplying by the inverse: [ 1.25 g x (mol/58.44 g) ]. This way, the unit of mol flips up to the numerator, and the units of grams cancel, leaving you with units of mol, as you are asked to find. Completing the calculation, you get 0.0214 mol of NaCl. A few points to pay attention to: always, always include units in your answer. Does your teacher care about significant figures? If so, the given data (1.25 g) has 3 significant figures. The answer of "0.0214 mol" has 3 significant figures as well (remember that the zeroes in front are not significant; they just hold the decimal place. You need to round up, since the calculator gives you an answer of "0.021389". If you want to report this number in scientific notation, it would be 2.14 x 10^-2 mol. Does your answer address the question asked? Keeping track of units helps. Reread the original question: you are asked for moles. Look at your answer: it has units of moles. Finally, make sure your answer makes sense. The grams of sodium chloride is much less than the molar mass, so you would expect to have less than one mole.
Given the following two equations, report the values of x and y. 3x + y = 15; x + 2y = 10.
Solving two equations with two unknowns is a common type of problem which can be solved by the method of substitution: solve one equation for one variable, then insert the solution into the other equation to solve for that variable. Once the value for the first variable is known, that value can be plugged into either equation to find the value for the other variable. Remember a primary rule of algebra: whatever you do to one side of the equation, you must do to the other side. For the above problem, we could solve the first equation for y as follows: subtract 3x from both sides, to get y = 15 - 3x. Next, substitute this expression (15-3x) into the second equation in place of y: x + 2(15-3x) = 10. This equation has only one variable - x - so we can find the value for x. First, distribute the 2 over the parentheses: x + 30 - 6x = 10. Combine like terms: -5x + 30 = 10. Subtract 30 from both sides to get -5x = -20. Divide both sides by -5 to find out that x = 4. Now, plug this value of x into either of the equations to find the value of y. Plugging into the first equation, you get 3(4) + y = 15 which simplifies to 12 + y = 15. Subtract 12 from both sides to get y = 3. It's always a good idea to double-check your answer. You can plug the values of x and y that you have found into either equation to make sure you get a true statement. For example, plugging x = 4 and y = 3 into x + 2y = 10 gives 4 + 2(3) = 10, which is a true statement. Therefore, the solution is correct.