|MadSci Network: Chemistry|
Greetings, Bethany: I will assume that you encountered this experiment in a textbook, and not in a laboratory. The reason I assume this relates to your statement that no water is used, when you immediately afterwards include the phrase "each 2mol dm-3". This leads me to take the time to try to clarify the description of the experiment. So: The "dm-3" portion of that translates (assuming that the 3 is an exponent) as "per cubic decimeter". Since a decimeter is a tenth of a meter, it is the same as ten centimeters. Also, since it happens that a liter is a cube that is ten centimeters on a side, it follows that "dm-3" can just as easily be translated as "per liter". So if we have 2 moles of HNO3 per liter, and we have 2 moles of NaOH per liter, then we are probably talking about liters of water. Chemists seldom use liters of air in their reactions! And when they DO use air, or some substance other than water, they ALWAYS say so. Also, please note that pure NaOH (for example) is a solid substance. Two moles of sodium hydroxide has a mass of only about 56 grams. By itself, it does NOT occupy a liter of space! This is one major reason why water is involved in so many chemists' reactions: It acts as a "space-filler". If we want to react X grams of Substance A with Y grams of Substance B, but one of these substances occupies ten times the volume of the other, how can we mix them simply and thoroughly? The answer chosen is to use water. The unequal volumes of the two substances can be separately mixed with amounts of water that ARE equal. Other reasons to use water include the fact that most substances don't chemically react with water, the fact that a great many substances mix very thoroughly indeed with water, AND the fact that when something dissolves in water, the total volume of liquid hardly increases at all! (There is space between water molecules, which can accommodate molecules of other substances.) Such a mixture is usually called a "solution", but occasionally you may need to refer to the mixture as a "suspension". (Note: you DO have to be concerned about changes in the volume of water, if you are working with suspensions.) So, if we take the average Substance A and mix it with water, Substance A becomes very evenly distributed throughout the volume of space occupied by the water -- and that's all. Since they probably won't chemically react, Substance A remains Substance A. Now do the same for Substance B ... and when the two volumes of water are mixed together, we KNOW that Substances A and B are being thoroughly mixed with each other! Next, you specifically mentioned "(ml)=25", which is a standard reference to 25 milliliters. A milliliter is a cube one centimeter on a side, and is defined as being one thousandth of a liter. Since a liter measures 10x10x10 centimeters, it should be obvious that there are a thousand cubic centimeters in a liter. Also/again, whenever chemists describe a measurement such as 25 milliliters, if they don't specify some substance other than water, then it is usually quite safe for you to assume that they ARE describing some mixture that is mostly water. Two more reasons that water is used so often: It is easy to manipulate in precise volumes, and it has a large "specific heat" (the amount of heat energy it takes to change the temperature of a unit mass of substance by one degree -- usually Celsius or degrees C). Those two factors let us "scale" the rate of a chemical reaction. If two subtances happen to react with so much violence as to destroy laboratory equipment, we can simply diulte the substances with so much water that their reaction becomes safely measurable, in a highly controlled way. Enough clarification; on to your Question, concerning how to find the energy released per mole -- which stll needs a bit of clarification! A mole of what? Hydrogen nitrate (more often called "nitric acid") or sodium hydroxide? Many chemical reactions are not so convenient as this one, in which one mole of each of the two substances will react COMPLETELY, when mixed. Historically, when chemists simply didn't know outcomes such as this in advance, they had a simple answer: Pick one! Pick a mole of some substance, and let it react completely with some other substance, and measure the energy. The heat released can then be described in terms of that single mole of the selected substance. (Afterwards, the resulting chemical compound(s) can be studied to learn exactly what sort of reaction occurred, and how many moles were involved, of the other substance.) So, since this particular case has a one-to-one ratio of involved moles of substances, the "per mole" in your Question can refer to EITHER the hydrogen nitrate or the sodium hydroxide. Feel free to pick one! The experiment describes using 25 milliliters of each of nitric acid and sodium hydroxide solutions. So the total volume of water is 50 milliliters, which conveniently has a mass of 50 grams. And that is your mass of water; its temperature change you gave as 6.5, which would be degrees Celsius (the mystery C in your Question). Next, since 25 milliliters is 1/40 of a liter, and since for each chemical reactant two moles were mixed with one liter of water, it follows that the reaction in the 50 ml of water involved 1/20 of a mole of each of hydrogen nitrate and sodium hydroxide. Finally, after you do the energy computation which you already know, you simply mulitply that by 20 to get your desired Answer.
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