Measurement, Problem Solving, and the Mole

Measurement - Units Common English-Metric Conversion Factors 2.54 cm = 1 inch 1 lb = g 1 qt = 943 mL

Measurements Prefixes Commonly used in Chemistry: prefix namesymbolvalue exponential notation kilo k1, centi c1/100 or milli m1/1,000 or micro µ nano n10 -9 pico p10 -12

Measurement - Temperature In the chemistry lab, temperature is measured in degrees Celsius or Centigrade. The temperature in Kelvins is found by adding The Fahrenheit scale has 180 o F/100 o C. This is reason for the 5/9 or 9/5 in the conversion formulas.

Significant Figures When writing a number, the certainty with which the number is known should be reflected in the way it is written. Digits which are the result of measurement or are known with a degree of certainty are called significant digits or significant figures.

Significant Figures The goal of paying attention to significant figures is to make sure that every number accurately reflects the degree of certainty or precision to which it is known. Likewise, when calculations are performed, the final result should reflect the same degree of certainty as the least certain quantity in the calculation.

Significant Figures If someone says “There are roughly a hundred students enrolled in the freshman chemistry course,” the enrollment should be written as 100 or 1 x Either notation indicates that the number is approximate, with only one significant figure.

Significant Figures If the enrollment is exactly one hundred students, the number should be written with a decimal point, as 100., or 1.00 x Note that in either form, the number has three significant figures.

Significant Figures The rules for counting significant figures: 1. Any non-zero integer is a significant figure.

Significant Figures 2. Zeros may be significant, depending upon where they appear in a number. a) Leading zeros (one that precede any non- zero digits) are not significant. For example, in , the first two zeros are not significant. They only serve to place the decimal point.

Significant Figures – Zeros (cont’d) b) Zeros between non-zero integers are always significant. In the number , the zero between the 2 and the 8 is a significant digit. c) Zeros at the right end of a number are significant only if the number contains a decimal point. In the number , the last zero is the result of a measurement, and is significant.

Significant Figures Thus, the number has four significant figures. If written in scientific notation, all significant digits must appear. So becomes x

Significant Figures 3. Exact numbers have an unlimited number of significant figures. Examples are 100cm = 1m, the “2” in the formula 2πr, or the number of atoms of a given element in the formula of a compound, such as the “2” in H 2 O. Using an exact number in a calculation will not limit the number of significant figures in the final result.

Significant Figures - Calculations When calculations are performed, the final result should reflect the same degree of certainty as the least certain quantity in the calculation. That is, the least certain quantity will influence the degree of certainty in the final result of the calculation.

Significant Figures - Calculations There are two sets of rules when performing calculations. One for addition and subtraction, and the other for multiplication and division. For Multiplication and Division: For Multiplication and Division: The result of the calculation should have the same number of significant figures as the least precise measurement used in the calculation.

Significant Figures - Calculations Multiplication & Division: Example: Determine the density of an object with a volume of 5.70 cm 3 and a mass of grams.

Significant Figures - Calculations Multiplication & Division: Example: Determine the density of an object with a volume of 5.70 cm 3 and a mass of grams. δ = mass/volume = g/5.70 cm 3 δ = = 1.56 g/cm 3

Significant Figures - Calculations Addition and Subtraction: Addition and Subtraction: The result has the same number of places after the decimal as the least precise measurement in the calculation. For example, calculate the sum of: g g g = = 25.02g

Significant Figures - Measurement All measurements involve some degree of uncertainty. When reading a mass from a digital analytical balance, the last digit (usually one-ten thousandth of a gram) is understood to be uncertain. All measurements involve some degree of uncertainty. When reading a mass from a digital analytical balance, the last digit (usually one-ten thousandth of a gram) is understood to be uncertain. When using other devices in the laboratory, such as a ruler, graduated cylinder, buret, etc., you should estimate one place beyond the smallest divisions on the device. When using other devices in the laboratory, such as a ruler, graduated cylinder, buret, etc., you should estimate one place beyond the smallest divisions on the device.

Significant Figures - Measurements The volume should be estimated to the nearest hundredth of a milliliter, since the buret is marked in tenths of a milliliter. The correct reading is (or or 20.16) mL. It is understood that the last number is uncertain.

Significant Figures - Measurements The value of mL indicates a volume in between 20.1 mL and 20.2 mL. If the liquid level were resting right on one of the divisions, the reading should reflect this by ending in a zero.

Conversion of Units Many chemical calculations involve the conversion of units. An example is calculating how many grams of a product can be obtained from a given mass of a reactant. The calculation involves going from mass of reactant to moles of reactant to moles of product to grams of product. You should write in your units for all calculations, and make sure they cancel properly.

Metric Conversion Factors These conversion factors are useful and worth learning. 1 inch = 2.54 cm 1 lb = g 1 L = qt

Problem The density of mercury is 13.6 g/mL. What is the weight, in lbs, of a quart of mercury?

Accuracy & Precision Most experiments are performed several times to help ensure that the results are meaningful. A single experiment might provide an erroneous result if there is an equipment failure or if a sample is contaminated. By performing several trials, the results may be more reliable.

Accuracy & Precision If the experimental values are close to the actual value (if it is known), the data is said to be accurate. If the experimental values are all very similar and reproducible, the data is said to be precise. The goal in making scientific measurements is to that the data be both accurate and precise.

Accuracy & Precision Data can be precise, but inaccurate. If a faulty piece of equipment or a contaminated sample is used for all trials, the data may be in agreement (precise), but inaccurate. Such an error is called a systematic error. If the scientist has good technique, the results will be similar, but too high or too low due to the systematic error.

Random Error In many experiments, data varies a bit with each trial. The variation in the results is due to random error. Examples might be estimating the last digit for the volume in a buret. Random errors have an equal probability of being too high or too low. As a result, if enough trials are performed, the random error will average itself out.

Moles Many chemical reactions are carried out using a few grams of each reactant. Such quantities contain huge numbers (on the order of ) of atoms or molecules. Many chemical reactions are carried out using a few grams of each reactant. Such quantities contain huge numbers (on the order of ) of atoms or molecules. A unit of quantity of matter, the mole, was established. A mole is defined as the number of carbon atoms in exactly 12 grams of 12 C. A unit of quantity of matter, the mole, was established. A mole is defined as the number of carbon atoms in exactly 12 grams of 12 C. Avogadro determined the number of particles (atoms or molecules) in a mole. Avogadro determined the number of particles (atoms or molecules) in a mole.

Moles Avogadro’s number = x particles/mole Avogadro’s number = x particles/mole Atoms are so small, that a mole of most substances can be easily held in ones hand. Atoms are so small, that a mole of most substances can be easily held in ones hand. Cu Al Hg Fe I2I2 S

Moles If we consider objects we can see, a mole of pennies would cover the entire planet and be 300 meters deep! However, the collection of atoms, called a mole, is very convenient in the laboratory (just like dozens are useful in buying eggs or pencils). If we consider objects we can see, a mole of pennies would cover the entire planet and be 300 meters deep! However, the collection of atoms, called a mole, is very convenient in the laboratory (just like dozens are useful in buying eggs or pencils).

Moles A mole of any atom has a mass equal to the element’s atomic mass expressed in grams. A mole of any atom has a mass equal to the element’s atomic mass expressed in grams. A mole of iron atoms has a mass of grams; a mole of iodine molecules (I 2 ) has a mass of (126.9) (2) = grams.

Moles The masses of each molar sample are provided below. The masses of each molar sample are provided below. Cu = 63.55g Al=26.98g Hg = g Fe=55.85 g I 2 =253.8 g S=32.07g

Molar Mass For compounds, once the formula is known, the mass of a mole of the substance can be calculated by summing up the masses of all the atoms in the compound. For compounds, once the formula is known, the mass of a mole of the substance can be calculated by summing up the masses of all the atoms in the compound. For example, hydrogen peroxide has the formula H 2 O 2 : For example, hydrogen peroxide has the formula H 2 O 2 : 2H +2O = 2(1.008g) + 2(16.00g) = g/mol A mole of hydrogen peroxide has a mass of grams. A mole of hydrogen peroxide has a mass of grams.

Problem Determine the number of silver atoms in a 10.0 gram sample of silver.