Chemistry-Solution - CHAPTER 1 CHEMISTRY THE STUDY OF...

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Unformatted text preview: CHAPTER 1 CHEMISTRY: THE STUDY OF CHANGE Problem Categories Biological: 1.24, 1.48, 1.69, 1.70, 1.78, 1.84, 1.93, 1.95, 1.96, 1.97, 1.105. Conceptual: 1.3, 1.4, 1.11, 1.12, 1.15, 1.16, 1.54, 1.62, 1.89, 1.101, 1.103. Environmental: 1.70, 1.87, 1.89, 1.92, 1.98. Industrial: 1.51, 1.55, 1.72, 1.81, 1.91. Difficulty Level Easy: 1.3, 1.11, 1.13, 1.14, 1.15, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.29, 1.30, 1.31, 1.32, 1.33, 1.34, 1.54, 1.55, 1.63, 1.64, 1.77, 1.80, 1.84, 1.89, 1.91. Medium: 1.4, 1.12, 1.16, 1.35, 1.36, 1.37, 1.38, 1.39, 1.40, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 1.50, 1.51, 1.52, 1.53, 1.56, 1.57, 1.59, 1.60, 1.61, 1.62, 1.70, 1.71, 1.72, 1.73, 1.74, 1.75, 1.76, 1.78, 1.79, 1.81, 1.82, 1.83, 1.85, 1.94, 1.95, 1.96, 1.97, 1.98. Difficult: 1.58, 1.65, 1.66, 1.67, 1.68, 1.69, 1.86, 1.87, 1.88, 1.90, 1.92, 1.93, 1.99, 1.100, 1.101, 1.102, 1.103, 1.104, 1.105, 1.106. 1.3 (a) Quantitative. This statement clearly involves a measurable distance. (b) Qualitative. This is a value judgment. There is no numerical scale of measurement for artistic excellence. (c) Qualitative. If the numerical values for the densities of ice and water were given, it would be a quantitative statement. (d) Qualitative. Another value judgment. (e) Qualitative. Even though numbers are involved, they are not the result of measurement. 1.4 (a) hypothesis 1.11 (a) Chemical property. Oxygen gas is consumed in a combustion reaction; its composition and identity are changed. (b) Chemical property. The fertilizer is consumed by the growing plants; it is turned into vegetable matter (different composition). (c) Physical property. The measurement of the boiling point of water does not change its identity or composition. (d) Physical property. The measurement of the densities of lead and aluminum does not change their composition. (e) Chemical property. When uranium undergoes nuclear decay, the products are chemically different substances. (a) Physical change. The helium isn't changed in any way by leaking out of the balloon. (b) Chemical change in the battery. (c) Physical change. The orange juice concentrate can be regenerated by evaporation of the water. (d) Chemical change. Photosynthesis changes water, carbon dioxide, etc., into complex organic matter. (e) Physical change. The salt can be recovered unchanged by evaporation. 1.12 (b) law (c) theory 2 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 1.13 Li, lithium; F, fluorine; P, phosphorus; Cu, copper; As, arsenic; Zn, zinc; Cl, chlorine; Pt, platinum; Mg, magnesium; U, uranium; Al, aluminum; Si, silicon; Ne, neon. 1.14 (a) (f) K Pu 1.15 (a) element 1.16 (a) (d) (g) homogeneous mixture homogeneous mixture heterogeneous mixture 1.21 density = 1.22 Strategy: We are given the density and volume of a liquid and asked to calculate the mass of the liquid. Rearrange the density equation, Equation (1.1) of the text, to solve for mass. (b) (g) Sn S (c) (h) (b) compound (b) (e) (d) (i) Cr Ar (c) (e) B Hg element (d) element heterogeneous mixture (c) (f) Ba compound compound homogeneous mixture mass 586 g = = 3.12 g/mL volume 188 mL density = mass volume Solution: mass = density × volume mass of ethanol = 1.23 ? °C = (°F − 32°F) × 0.798 g × 17.4 mL = 13.9 g 1 mL 5°C 9°F 5°C = 35°C 9°F 5°C (12 − 32)°F × = − 11°C 9° F 5°C (102 − 32)°F × = 39°C 9°F 5°C (1852 − 32)°F × = 1011°C 9°F 9° F ⎞ ⎛ ⎜ °C × 5°C ⎟ + 32°F ⎝ ⎠ (a) ? °C = (95 − 32)°F × (b) ? °C = (c) ? °C = (d) ? °C = (e) ? °F = 9° F ⎞ ⎛ ? °F = ⎜ −273.15 °C × + 32°F = − 459.67°F 5°C ⎟ ⎝ ⎠ 1.24 Strategy: Find the appropriate equations for converting between Fahrenheit and Celsius and between Celsius and Fahrenheit given in Section 1.7 of the text. Substitute the temperature values given in the problem into the appropriate equation. (a) Conversion from Fahrenheit to Celsius. ? °C = (°F − 32°F) × 5°C 9°F CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE ? °C = (105 − 32)°F × (b) 5°C = 41°C 9°F Conversion from Celsius to Fahrenheit. 9° F ⎞ ⎛ ? °F = ⎜ °C × + 32°F 5°C ⎟ ⎝ ⎠ 9° F ⎞ ⎛ ? °F = ⎜ −11.5 °C × + 32°F = 11.3 °F 5°C ⎟ ⎝ ⎠ (c) Conversion from Celsius to Fahrenheit. 9° F ⎞ ⎛ + 32°F ? °F = ⎜ °C × 5°C ⎟ ⎝ ⎠ 9 °F ⎞ ⎛ + 32°F = 1.1 × 104 °F ? °F = ⎜ 6.3 × 103 °C × 5°C ⎟ ⎝ ⎠ (d) Conversion from Fahrenheit to Celsius. ? °C = (°F − 32°F) × 5°C 9°F ? °C = (451 − 32)°F × 1.25 K = (°C + 273°C) 5°C = 233°C 9°F 1K 1°C (a) K = 113°C + 273°C = 386 K (b) K = 37°C + 273°C = 3.10 × 10 K (c) K = 357°C + 273°C = 6.30 × 10 K (a) 1K 1°C °C = K − 273 = 77 K − 273 = −196°C (b) °C = 4.2 K − 273 = −269°C (c) °C = 601 K − 273 = 328°C 1.29 (a) 2.7 × 10 1.30 (a) 10 1.26 2 2 K = (°C + 273°C) −2 −8 (b) 3.56 × 10 2 10 −8 4 4.7764 × 10 (d) indicates that the decimal point must be moved two places to the left. 1.52 × 10 (b) (c) −2 = 0.0152 indicates that the decimal point must be moved 8 places to the left. 7.78 × 10 −8 = 0.0000000778 9.6 × 10 −2 3 4 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 1.31 (a) (b) −1 2 145.75 + (2.3 × 10 ) = 145.75 + 0.23 = 1.4598 × 10 79500 2.5 × 10 2 = 7.95 × 104 2.5 × 10 2 −3 = 3.2 × 102 −4 −3 −3 −3 (c) (d) 1.32 (7.0 × 10 ) − (8.0 × 10 ) = (7.0 × 10 ) − (0.80 × 10 ) = 6.2 × 10 (1.0 × 10 ) × (9.9 × 10 ) = 9.9 × 10 (a) Addition using scientific notation. 4 10 6 n Strategy: Let's express scientific notation as N × 10 . When adding numbers using scientific notation, we must write each quantity with the same exponent, n. We can then add the N parts of the numbers, keeping the exponent, n, the same. Solution: Write each quantity with the same exponent, n. 3 n 3 Let’s write 0.0095 in such a way that n = −3. We have decreased 10 by 10 , so we must increase N by 10 . Move the decimal point 3 places to the right. 0.0095 = 9.5 × 10 −3 Add the N parts of the numbers, keeping the exponent, n, the same. −3 9.5 × 10 −3 + 8.5 × 10 −3 18.0 × 10 The usual practice is to express N as a number between 1 and 10. Since we must decrease N by a factor of 10 n to express N between 1 and 10 (1.8), we must increase 10 by a factor of 10. The exponent, n, is increased by 1 from −3 to −2. 18.0 × 10 (b) −3 −2 = 1.8 × 10 Division using scientific notation. n Strategy: Let's express scientific notation as N × 10 . When dividing numbers using scientific notation, divide the N parts of the numbers in the usual way. To come up with the correct exponent, n, we subtract the exponents. Solution: Make sure that all numbers are expressed in scientific notation. 2 653 = 6.53 × 10 Divide the N parts of the numbers in the usual way. 6.53 ÷ 5.75 = 1.14 Subtract the exponents, n. 1.14 × 10 (c) +2 − (−8) = 1.14 × 10 +2 + 8 = 1.14 × 10 10 Subtraction using scientific notation. n Strategy: Let's express scientific notation as N × 10 . When subtracting numbers using scientific notation, we must write each quantity with the same exponent, n. We can then subtract the N parts of the numbers, keeping the exponent, n, the same. CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 5 Solution: Write each quantity with the same exponent, n. Let’s write 850,000 in such a way that n = 5. This means to move the decimal point five places to the left. 850,000 = 8.5 × 10 5 Subtract the N parts of the numbers, keeping the exponent, n, the same. 5 8.5 × 10 5 − 9.0 × 10 −0.5 × 10 5 The usual practice is to express N as a number between 1 and 10. Since we must increase N by a factor of 10 n to express N between 1 and 10 (5), we must decrease 10 by a factor of 10. The exponent, n, is decreased by 1 from 5 to 4. 5 −0.5 × 10 = −5 × 10 (d) 4 Multiplication using scientific notation. n Strategy: Let's express scientific notation as N × 10 . When multiplying numbers using scientific notation, multiply the N parts of the numbers in the usual way. To come up with the correct exponent, n, we add the exponents. Solution: Multiply the N parts of the numbers in the usual way. 3.6 × 3.6 = 13 Add the exponents, n. 13 × 10 −4 + (+6) = 13 × 10 2 The usual practice is to express N as a number between 1 and 10. Since we must decrease N by a factor of 10 n to express N between 1 and 10 (1.3), we must increase 10 by a factor of 10. The exponent, n, is increased by 1 from 2 to 3. 2 3 13 × 10 = 1.3 × 10 1.33 (a) (e) four three 1.34 (a) (e) one two or three 1.35 (a) 10.6 m 1.36 (b) (f) (a) Division (b) (f) (b) (c) (g) three one 0.79 g (c) five one (c) (g) two one three one or two 2 16.5 cm (d) (h) two, three, or four two (d) (d) four 6 3 1 × 10 g/cm Strategy: The number of significant figures in the answer is determined by the original number having the smallest number of significant figures. Solution: 7.310 km = 1.283 5.70 km The 3 (bolded) is a nonsignificant digit because the original number 5.70 only has three significant digits. Therefore, the answer has only three significant digits. The correct answer rounded off to the correct number of significant figures is: 1.28 (Why are there no units?) 6 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE (b) Subtraction Strategy: The number of significant figures to the right of the decimal point in the answer is determined by the lowest number of digits to the right of the decimal point in any of the original numbers. Solution: Writing both numbers in decimal notation, we have 0.00326 mg − 0.0000788 mg 0.0031812 mg The bolded numbers are nonsignificant digits because the number 0.00326 has five digits to the right of the decimal point. Therefore, we carry five digits to the right of the decimal point in our answer. The correct answer rounded off to the correct number of significant figures is: −3 0.00318 mg = 3.18 × 10 (c) mg Addition Strategy: The number of significant figures to the right of the decimal point in the answer is determined by the lowest number of digits to the right of the decimal point in any of the original numbers. Solution: Writing both numbers with exponents = +7, we have 7 7 7 (0.402 × 10 dm) + (7.74 × 10 dm) = 8.14 × 10 dm 7 Since 7.74 × 10 has only two digits to the right of the decimal point, two digits are carried to the right of the decimal point in the final answer. (d) Subtraction, addition, and division Strategy: For subtraction and addition, the number of significant figures to the right of the decimal point in that part of the calculation is determined by the lowest number of digits to the right of the decimal point in any of the original numbers. For the division part of the calculation, the number of significant figures in the answer is determined by the number having the smallest number of significant figures. First, perform the subtraction and addition parts to the correct number of significant figures, and then perform the division. Solution: (7.8 m − 0.34 m) 7.5 m = = 3.8 m /s (1.15 s + 0.82 s) 1.97 s 1.37 Calculating the mean for each set of date, we find: Student A: 87.6 mL Student B: 87.1 mL Student C: 87.8 mL From these calculations, we can conclude that the volume measurements made by Student B were the most accurate of the three students. The precision in the measurements made by both students B and C are fairly high, while the measurements made by student A are less precise. In summary: Student A: neither accurate nor precise Student B: both accurate and precise Student C: precise, but not accurate CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 1.38 7 Calculating the mean for each set of date, we find: Tailor X: 31.5 in Tailor Y: 32.6 in Tailor Z: 32.1 in From these calculations, we can conclude that the seam measurements made by Tailor Z were the most accurate of the three tailors. The precision in the measurements made by both tailors X and Z are fairly high, while the measurements made by tailor Y are less precise. In summary: Tailor X: most precise Tailor Y: least accurate and least precise Tailor Z: most accurate 1 dm = 226 dm 0.1 m (a) ? dm = 22.6 m × (b) ? kg = 25.4 mg × (c) 1.39 ? L = 556 mL × (d) 1.40 ? g cm 3 0.001 g 1 kg × = 2.54 × 10−5 kg 1 mg 1000 g 1 × 10−3 L = 0.556 L 1 mL 3 = 1000 g ⎛ 1 × 10−2 m ⎞ × ×⎜ ⎟ = 0.0106 g/cm 3 ⎜ 1 cm ⎟ 1 kg 1 m3 ⎝ ⎠ 10.6 kg (a) Strategy: The problem may be stated as ? mg = 242 lb A relationship between pounds and grams is given on the end sheet of your text (1 lb = 453.6 g). This relationship will allow conversion from pounds to grams. A metric conversion is then needed to convert −3 grams to milligrams (1 mg = 1 × 10 g). Arrange the appropriate conversion factors so that pounds and grams cancel, and the unit milligrams is obtained in your answer. Solution: The sequence of conversions is lb → grams → mg Using the following conversion factors, 453.6 g 1 lb 1 mg 1 × 10−3 g we obtain the answer in one step: ? mg = 242 lb × 453.6 g 1 mg × = 1.10 × 108 mg 1 lb 1 × 10−3 g Check: Does your answer seem reasonable? Should 242 lb be equivalent to 110 million mg? How many mg are in 1 lb? There are 453,600 mg in 1 lb. 8 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE (b) Strategy: The problem may be stated as 3 3 ? m = 68.3 cm Recall that 1 cm = 1 × 10 −2 3 3 m. We need to set up a conversion factor to convert from cm to m . Solution: We need the following conversion factor so that centimeters cancel and we end up with meters. 1 × 10−2 m 1 cm Since this conversion factor deals with length and we want volume, it must therefore be cubed to give 3 ⎛ 1 × 10−2 m ⎞ 1 × 10−2 m 1 × 10−2 m 1 × 10−2 m × × =⎜ ⎟ ⎜ 1 cm ⎟ 1 cm 1 cm 1 cm ⎝ ⎠ We can write 3 ⎛ 1 × 10−2 m ⎞ ? m = 68.3 cm × ⎜ ⎟ = 6.83 × 10−5 m 3 ⎜ 1 cm ⎟ ⎝ ⎠ 3 3 −6 3 Check: We know that 1 cm = 1 × 10 −6 −5 1 × 10 gives 6.83 × 10 . 3 1 3 m . We started with 6.83 × 10 cm . Multiplying this quantity by (c) Strategy: The problem may be stated as 3 ? L = 7.2 m 3 3 3 In Chapter 1 of the text, a conversion is given between liters and cm (1 L = 1000 cm ). If we can convert m 3 −2 to cm , we can then convert to liters. Recall that 1 cm = 1 × 10 m. We need to set up two conversion 3 3 3 factors to convert from m to L. Arrange the appropriate conversion factors so that m and cm cancel, and the unit liters is obtained in your answer. Solution: The sequence of conversions is 3 3 m → cm → L Using the following conversion factors, 3 ⎛ 1 cm ⎞ ⎜ ⎟ ⎜ 1 × 10−2 m ⎟ ⎝ ⎠ 1L 1000 cm3 the answer is obtained in one step: 3 ⎛ 1 cm ⎞ 1L = 7.2 × 103 L ? L = 7.2 m × ⎜ ⎟× ⎜ 1 × 10−2 m ⎟ 1000 cm3 ⎝ ⎠ 3 3 3 3 Check: From the above conversion factors you can show that 1 m = 1 × 10 L. Therefore, 7 m would 3 equal 7 × 10 L, which is close to the answer. CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 9 (d) Strategy: The problem may be stated as ? lb = 28.3 μg A relationship between pounds and grams is given on the end sheet of your text (1 lb = 453.6 g). This relationship will allow conversion from grams to pounds. If we can convert from μg to grams, we can then −6 convert from grams to pounds. Recall that 1 μg = 1 × 10 g. Arrange the appropriate conversion factors so that μg and grams cancel, and the unit pounds is obtained in your answer. Solution: The sequence of conversions is μg → g → lb Using the following conversion factors, 1 × 10−6 g 1 μg 1 lb 453.6 g we can write ? lb = 28.3 μg × 1 × 10−6 g 1 lb × = 6.24 × 10−8 lb 1 μg 453.6 g Check: Does the answer seem reasonable? What number does the prefix μ represent? Should 28.3 μg be a very small mass? 1.41 1255 m 1 mi 3600 s × × = 2808 mi/h 1s 1609 m 1h 1.42 Strategy: The problem may be stated as ? s = 365.24 days You should know conversion factors that will allow you to convert between days and hours, between hours and minutes, and between minutes and seconds. Make sure to arrange the conversion factors so that days, hours, and minutes cancel, leaving units of seconds for the answer. Solution: The sequence of conversions is days → hours → minutes → seconds Using the following conversion factors, 24 h 1 day 60 min 1h 60 s 1 min we can write ? s = 365.24 day × 24 h 60 min 60 s × × = 3.1557 × 107 s 1 day 1h 1 min Check: Does your answer seem reasonable? Should there be a very large number of seconds in 1 year? 1.43 (93 × 106 mi) × 1.609 km 1000 m 1s 1 min × × × = 8.3 min 8 1 mi 1 km 60 s 3.00 × 10 m 10 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 1.44 (a) ? in/s = (b) ? m/min = (c) ? km/h = 1 mi 5280 ft 12 in 1 min × × × = 81 in/s 13 min 1 mi 1 ft 60 s 1 mi 1609 m × = 1.2 × 102 m/min 13 min 1 mi 1 mi 1609 m 1 km 60 min × × × = 7.4 km/h 13 min 1 mi 1000 m 1h 6.0 ft × 1m = 1.8 m 3.28 ft 168 lb × 1.45 453.6 g 1 kg × = 76.2 kg 1 lb 1000 g 55 mi 1.609 km × = 88 km/h 1h 1 mi 1.46 ? km/h = 1.47 62 m 1 mi 3600 s × × = 1.4 × 102 mph 1s 1609 m 1h 1.48 0.62 ppm Pb = 1.49 (a) 1.42 yr × 365 day 24 h 3600 s 3.00 × 108 m 1 mi × × × × = 8.35 × 1012 mi 1 yr 1 day 1h 1s 1609 m (b) 32.4 yd × 36 in 2.54 cm × = 2.96 × 103 cm 1 yd 1 in (c) 3.0 × 1010 cm 1 in 1 ft × × = 9.8 × 108 ft/s 1s 2.54 cm 12 in (a) ? m = 185 nm × (b) ? s = (4.5 × 109 yr) × (c) ⎛ 0.01 m ⎞ −5 3 ? m 3 = 71.2 cm3 × ⎜ ⎟ = 7.12 × 10 m 1 cm ⎠ ⎝ (d) ⎛ 1 cm ⎞ 1L = 8.86 × 104 L ? L = 88.6 m × ⎜ ⎟× ⎜ 1 × 10−2 m ⎟ 1000 cm3 ⎝ ⎠ 1.50 0.62 g Pb 1 × 106 g blood 0.62 g Pb 6.0 × 103 g of blood × = 3.7 × 10−3 g Pb 6 1 × 10 g blood 1 × 10−9 m = 1.85 × 10−7 m 1 nm 365 day 24 h 3600 s × × = 1.4 × 1017 s 1 yr 1 day 1h 3 3 3 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 11 3 ⎛ 1 cm ⎞ 1 kg 3 3 ×⎜ ⎟ = 2.70 × 10 kg/m 1000 g ⎝ 0.01 m ⎠ 1.51 density = 2.70 g 1.52 density = 0.625 g 1L 1 mL × × = 6.25 × 10−4 g/cm 3 1L 1000 mL 1 cm3 1.53 Substance (a) water (b) carbon (c) iron (d) hydrogen gas (e) sucrose (f) table salt (g) mercury (h) gold (i) air 1.54 See Section 1.6 of your text for a discussion of these terms. 1 cm3 × Qualitative Statement colorless liquid black solid (graphite) rusts easily colorless gas tastes sweet tastes salty liquid at room temperature a precious metal a mixture of gases Quantitative Statement freezes at 0°C 3 density = 2.26 g/cm 3 density = 7.86 g/cm melts at −255.3°C at 0°C, 179 g of sucrose dissolves in 100 g of H2O melts at 801°C boils at 357°C 3 density = 19.3 g/cm contains 20% oxygen by volume (a) Chemical property. Iron has changed its composition and identity by chemically combining with oxygen and water. (b) Chemical property. The water reacts with chemicals in the air (such as sulfur dioxide) to produce acids, thus changing the composition and identity of the water. Physical property. The color of the hemoglobin can be observed and measured without changing its composition or identity. Physical property. The evaporation of water does not change its chemical properties. Evaporation is a change in matter from the liquid state to the gaseous state. Chemical property. The carbon dioxide is chemically converted into other molecules. (c) (d) (e) 1 ton = 4.75 × 107 tons of sulfuric acid 1.55 (95.0 × 109 lb of sulfuric acid) × 1.56 Volume of rectangular bar = length × width × height density = 1.57 2.0 × 10 lb 3 52.7064 g m = = 2.6 g/cm 3 (8.53 cm)(2.4 cm)(1.0 cm) V mass = density × volume (a) 3 mass = (19.3 g/cm ) × [ 4 3 4 π(10.0 cm) ] = 8.08 × 10 g 3 3 (b) (c) ⎛ 1 cm ⎞ −6 mass = (21.4 g/cm3 ) × ⎜ 0.040 mm × ⎟ = 1.4 × 10 g 10 mm ⎠ ⎝ mass = (0.798 g/mL)(50.0 mL) = 39.9 g 12 CHAPTER 1: CHEMISTRY--THE STUDY OF CHANGE 1.58 You are asked to solve for the inner diameter of the tube. If you can calculate the volume that the mercury 2 occupies, you can calculate the radius of the cylinder, Vcylinder = πr h (r is the inner radius of the cylinder, and h is the height of the cylinder). The cylinder diameter is 2r. volume of Hg filling cylinder = mass of Hg density of Hg 105.5 g volume of Hg filling cylinder = 13.6 g/cm 3 = 7.757 cm3 Next, solve for the radius of the cylinder. 2 Volume of cylinder = πr h r= volume π×h r= 7.757 cm3 = 0.4409 cm π × 12.7 cm The cylinder diameter equals 2r. Cylinder diameter = 2r = 2(0.4409 cm) = 0.882 cm 1.59 From the mass of the water and its density, we can calculate the volume that the water occupies. The volume that the water occupies is equal to the volume of the flask. volume = mass density Mass of water = 87.39 g − 56.12 g = 31.27 g Volume of the flask = mass 31.27 g = = 31.35 cm 3 density 0.9976 g/cm3 1.60 343 m 1 mi 3600 s × × = 767 mph 1s 1609 m 1h 1.61 The volume of silver is equal to the volume of water it displaces. 3 Volume...
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