A. Incorrect! Check your algebra when you solved for volume. B. Incorrect! Check your algebra when you solved for volume.

Transcription

1 AP Chemistry - Problem Drill 03: Basic Math for Chemistry No. 1 of Unlike math problems, chemistry calculations have two key elements to consider in any number units and significant figures. Solve the following problem for volume with the correct units and significant figures: g 15. 0g 2.5 ml volume (A) 37.5 ml (B) ml (C) 6.0 ml (D) 6.00 ml Check your algebra when you solved for volume. Check your algebra when you solved for volume. C. Correct! Good job! You solved for volume using algebra and you had two significant figures (the least number in the problem) as well as the correct volume unit. You solved for volume correctly, but check your significant figures. Multiply both sides by volume: g 15.0g ( Volume ) 2.5 Volume ml volume Divide both sides by the density: ( Volume ) 2.5 g ml 15.0g 2.5 g g ml 2.5 ml Calculate the answer: 15.0g Volume 6. 0mL 2.5 g ml The least number of significant figures in the problem is 2. Round the answer to 2 significant figures. The correct answer is (C).

2 No. 2 of Scientific notation is a way to write either very small or large numbers. One benefit of this form is that the significant figures are clearly defined in the format. Write the following number in scientific notation with 4 significant figures: (A) (B) (C) (D) The decimal point needs to be moved to be behind the first nonzero number for scientific notation. The problem asked for 4 significant figures, not 4 decimal places. C. Correct! Good job! With the requirement of 4 significant figures, the format is n.nnn x 10 m. You gave 4 significant figures with the correct scientific notation. The original number was large. Therefore you need the power of 10 to be positive. Move the decimal behind the first non-zero number: It moved 6 times to get there and the original number was big (>1), so the exponent is 6 Round to 4 significant figures: The correct answer is (C).

3 No. 3 of Scientific notation is in an exponent form. Many calculations in chemistry involve the operations of powers. Calculate the following: ( ) (A) 3 1 (B) 3 14 (C) 3 17 (D) 3-3 Rather than multiply and divide exponents, you need to add exponents when multiplying numbers and subtract the exponents when dividing numbers. Remember to add exponents when multiplying numbers with the same base and subtract when dividing. Be sure to subtract exponents when dividing numbers with the same base. D. Correct! Good job! You added the exponents when multiplying numbers with the same base and subtracted exponents when dividing. Add the exponents when multiplying with the same base: = 3 7 Subtract the exponents when dividing: = 3-3 The correct answer is (D).

4 No. 4 of The ph is defined as the decimal logarithm of the reciprocal of the hydrogen ion activity (or concentration), ph = -log[h 3 O + ]. What is [H 3 O + ] if ph = 8.7? (A) (B) (C) (D) ph = 8.7 = -log[h 3 O + ]. If y = log x then x = 10 -y ph = 8.7 = -log[h 3 O + ]. If y = log x then x = 10 -y ph = 8.7 = -log[h 3 O + ]. If y = log x then x = 10 -y D. Correct! Good job! ph = 8.7 = -log[h 3 O + ]. If y = log x then x = 10 -y If y = -log x Then x = 10 -y Where y = 8.7 and x = [H 3 O + ] [H 3 O + ] = The correct answer is (D).

5 No. 5 of The ability to properly calculate operations in scientific notation format using a scientific calculator is the basic skill in chemistry. Use your calculator to solve the following: (A) (B) (C) (D) A. Correct! Good job! Use the EE button when calculating scientific notation and the divide key each time you re on the bottom of the expression. Use the EE button when calculating scientific notation and the divide key each time you re on the bottom of the expression. Use the EE button when calculating scientific notation and the divide key each time you re on the bottom of the expression. Use the EE button when calculating scientific notation and the divide key each time you re on the bottom of the expression. Use the EE button when calculating scientific notation and the divide key each time you re on the bottom of the expression. Enter: 2.5EE6 3.72EE EE EE3 = 6.1EE-11 The correct answer is (A).

6 No. 6 of When combining measurements with various degrees of precision, the precision of the final answer can be no greater than the least precise measurement. This basic principle of measurement leads to a very simple rule for addition and subtraction in terms of significant figures. When measurements are added or subtracted, the result can contain no more decimal places than the least precise measurement. Give the answer to the following volumetric measurements with the correct number of significant figures: =? (A) (B) (C) 260 (D) A. Correct! Good job! When adding and subtracting, the answer needs to have the least number of decimal places among those given measurements. When adding and subtracting, the answer needs to have the least number of decimal places among those given measurements. When adding and subtracting, the answer needs to have the least number of decimal places among those given measurements. When adding and subtracting, the answer needs to have the least number of decimal places among those given measurements. When adding and subtracting, the result needs to have the least number of decimal places among the original measurements = The least number of decimal places in the problem is 1. Round the answer to 1 decimal place The correct answer is (A).

7 No. 7 of Acidity can be measured by ph, the lower ph value and the more acidic of a solution. A solution with a ph of 3 is how many times more acidic than a solution with a ph of 5 if ph is a log 10 scale? (A) 2 (B) 20 (C) 10 (D) 100 Each change of 1 in ph is a change of 10x in concentration. Each change of 1 in ph is a change of 10x in concentration. Each change of 1 in ph is a change of 10x in concentration. D. Correct! Good job! Each change of 1 in ph is a change of 10x in concentration of H + ion. Hence 10x10 = 100 folds more acidic in ph=3 than ph=5. You can also calculate this by ph = 5-3 = 2, therefore [H 3 O + ] = 10 2 = 100. Each change of 1 in ph is a change of 10x in concentration. If the ph changes from 3 to 5, there is a change of 2. This means there is a change of = 100 in the concentration. The correct answer is (D).

8 No. 8 of If the power is negative in a scientific notation, this indicates a small number of less than 1, vice versa with the positive power. Write out the following number: (A) (B) (C) (D) The negative exponent of 10 indicates a tiny number, not a large one. The negative exponent of 10 indicates a tiny number, not a large one. Count how many times you moved the decimal again. D. Correct! Good job! The negative exponent indicates a tiny number and the decimal point is moved 5 times. The exponent is negative, so the number will be small (<1). Move the decimal place 5 times to the left to make the number tiny. As in all situations that require the use of mathematics, first THINK about the relative sizes of the numbers that you expect as an answer, BEFORE you start to do the calculations. This will help you to prevent many errors on exams, and in life. In this case, remove the exponent of -5, move the decimal place to the left and the original number in scientific notation becomes The correct answer is (D).

9 No. 9 of For a power of a power, you multiply the exponents, (x a ) b = x ab. Simplify ( ) 4. (A) (B) (C) (D) Don t forget to take the original number to the power as well as the exponent of the scientific notation. B. Correct! Good job! The number is taken to the exponent and the power of 10 is multiplied by the exponent. The number is taken to the exponent and the power of 10 is multiplied by the exponent. The number is taken to the exponent and the power of 10 is multiplied by the exponent. The number is taken to the exponent and the power of 10 is multiplied by the exponent. 2 4 = 16 and (10 3 ) 4 = The correct answer is (B).

10 No. 10 of Logarithmic calculations with significant figures have one rounding rule: The significant numbers in the fraction part of a logarithm (also called mantissa) = the number of significant figures in the resulting value. If the hydrogen concentration in a solution is , what is its ph value with proper significant figures? (A) ph = 1.25 (B) ph = 1.9 (C) ph = 1.90 (D) ph = 1.3 Good try, you need to take the -log operation of the given number. The calculation is correct but the number of significant figures is incorrect. Review the significant figure rule for logarithms. C. Correct! Good job! If [H 3 O + ] = 0.125, the ph = -log[h 3 O + ] = -log0.125 = Since the given logarithm has three significant figures in its fraction part, the end result should have three significant figures, according to the logarithmic significant figure rule. Good try, you need to take the -log operation of the given number. Also be aware of the significant figures. If [H 3 O + ] = 0.125, the ph = -log[h 3 O + ] = -log0.125 = Since the given logarithm has three significant figures in its fraction part, the end result should have three significant figures, according to the logarithmic significant figure rule. This gives the level of precision in the measurement. The correct answer is (C).