Physical Science Density Practice Problems PDF

LT 3 AND 4 lt4.pdf lt3.pdf Physical Science Density Practice Problems (lt4.pdf) Key Concepts: Density Formula: D=Vm​ D=mV Where ( D ) is density, ( m ) is mass, and ( V ) is vol...

LT 3 AND 4 lt4.pdf lt3.pdf Physical Science Density Practice Problems (lt4.pdf) Key Concepts: Density Formula: D=Vm​ D=mV Where ( D ) is density, ( m ) is mass, and ( V ) is volume. Units: Density is typically expressed in g/cm³ or g/mL. Practice Problems: Density of Tin: Mass = 16.52 g, Volume = 2.26 cm³ Density = 2.26cm316.52g​=7.31g/cm3 16.52 g2.26 cm3=7.31 g/cm3 Density of a Liquid: Mass = 163 g, Volume = 50.0 cm³ Density = 50.0cm3163g​=3.26g/cm3 163 g50.0 cm3=3.26 g/cm3 Density of Wood: Mass = 25 g, Volume = 35 cm³ LT 3 AND 4 1  Density = 35cm325g​=0.71g/cm3 (likely not oak) 25 g35 cm3=0.71 g/cm3 Mass of Pine: Volume = 800 cm³, Density = 0.5 g/cm³ Mass = 0.5g/cm3×800cm3=400g 0.5 g/cm3×800 cm3=400 g Volume of Metal: Mass = 325 g, Density = 9.0 g/cm³ Volume = 9.0g/cm3325g​=36.11cm3 325 g9.0 g/cm3=36.11 cm3 Mass of Water: Volume = 100 cm x 50 cm x 30 cm = 150,000 cm³ Mass = 150,000 g (since density of water = 1 g/cm³) Volume Displacement: Initial water level = 40.0 mL, Final = 63.4 mL Volume of copper = 63.4 mL - 40.0 mL = 23.4 mL Density of copper = 8.9 g/cm³, Mass = 8.9g/cm3×23.4cm3=208.26g 8.9 g/cm3×23.4 cm3=208.26 g Density of a Substance: Mass = 0.36 g, Volume = 2500 cm³ Density = 2500cm30.36g​=0.000144g/cm3 0.36 g2500 cm3=0.000144 g/cm3 Mass of Water: Volume = 75 mL Mass = 75 g (density of water = 1 g/mL) LT 3 AND 4 2  Understanding Accuracy and Precision in Scientific Measurement (lt3.pdf) Key Concepts: Accuracy: How close a measurement is to the true value. Precision: How close measurements are to each other, regardless of their closeness to the true value. Examples: Golf Analogy: Accurate shots land in the hole; precise shots land close together but not necessarily in the hole. Measurement Techniques: Measuring Length: Use a metric ruler; read in millimeters (mm) and centimeters (cm). Measuring Mass: Use a balance (triple beam or electronic) for accurate mass readings. Measuring Volume: Use a graduated cylinder; read the meniscus for accurate liquid volume. Systems of Measurement: SI Units: Standardized units used in scientific measurements (e.g., meter for length, kilogram for mass). Unit Conversions: Examples of converting between SI and English units, emphasizing the importance of using a consistent measurement system. LT 3 AND 4 3 Density  Density Density is the mass per unit of volume of a material. Units are g/mL or g/cm3 Different materials have different densities.  Density The equation for density is: How to use a Scientific Formula List the givens in the problem. Write the quantity, value, and units. Write the formula Rearrange the formula to solve for the unknown Plug in your numbers Solve – don’t forget units!  Density Problems 1. A block of aluminum has a mass of 8.1g and a volume of 3 cm3. What is the density of aluminum? Givens: m = 8.1 g V = 3 cm3 D=?  Density Problems 1. A block of aluminum has a mass of 8.1g and a volume of 3 cm3. What is the density of aluminum? Givens: Formula: m = 8.1 g V = 3 cm3 D=?  Density Problems 1. A block of aluminum has a mass of 8.1g and a volume of 3 cm3. What is the density of aluminum?  Density Problems 2. Water has a density of 1 g/mL. What is the mass of 75 mL of water?  Density Problems 3. A piece of iron has a mass of 31.6g. The density of iron is 7.9g/mL. What is its volume?  Density Problems 4. A sealed 2500 mL flask is full to capacity with 35 g of a substance. Determine the density of the substance.  Density Problems 5. Diamonds have a density of 3.5 g/cm3. how big is a diamond that has a mass of 1.0 g? [Figure 1] The man in this cartoon is filling balloons with helium gas. What will happen if he lets go of the filled balloons? They will rise up into the air until they reach the ceiling. Do you know why? It’s because helium has less density than air. Defining Density Density is an important physical property of matter. It reflects how closely packed the particles of matter are. When particles are packed together more tightly, matter has greater density. Differences in density of matter explain many phenomena, not just why helium balloons rise. For example, differences in density of cool and warm ocean water explain why currents such as the Gulf Stream flow through the oceans. To better understand density, think about a bowling ball and volleyball, pictured in the Figure below. Imagine lifting each ball. The two balls are about the same size, but the bowling ball feels much heavier than the volleyball. That’s because the bowling ball is made of solid plastic, which contains a lot of tightly packed particles of matter. The volleyball, in contrast, is full of air, which contains fewer, more widely spaced particles of matter. In other words, the matter inside the bowling ball is denser than the matter inside the volleyball. [Figure 2] A bowling ball is denser than a volleyball. Although both balls are similar in size, the bowling ball feels much heavier than the volleyball. Q: If you ever went bowling, you may have noticed that some bowling balls feel heavier than others even though they are the same size. How can this be? A: Bowling balls that feel lighter are made of matter that is less dense. Calculating Density The density of matter is actually the amount of matter in a given space. The amount of matter is measured by its mass, and the space matter takes up is measured by its volume. Therefore, the density of matter can be calculated with this formula: Density=massvolume Assume, for example, that a book has a mass of 500 g and a volume of 1000 cm3. Then the density of the book is: Density=500 g1000 cm3=0.5 g/cm3 Q: What is the density of a liquid that has a volume of 30 mL and a mass of 300 g? A: The density of the liquid is: Density=300 g30 mL=10 g/mL Summary Density is an important physical property of matter. It reflects how closely packed the particles of matter are. The density of matter can be calculated by dividing its mass by its volume. Review What is density? Find the density of an object that has a mass of 5 kg and a volume of 50 cm3. Create a sketch that shows the particles of matter in two substances that differ in density. Label the sketch to show which substance has greater density.  SI CONVERSION FACTORS Length SI Unit: meter (m) 1 m = 1000 mm 1 meter = 1.0936 yd 5280 ft = 1 mi 1 m = 100 cm 1 meter = 3.28 ft 12 in = 1ft 1000 m = 1 km 2.54 cm = 1 in (exact) 3 ft = 1 yd 1 m = 1 x 106 µm 1 mile = 1.6 km 1 m = 1 x 1010angstrom 1 km = 0.62137 mi 1 m = 1 x 109 nm Mass SI Unit: kilogram (kg) 1 kg = 1000 g 1 kg = 2.2046 lb 16 oz = 1 lb 1 g = 1000 mg 453.59 g = 1 lb 2000 lb = 1 ton 1Metric ton = 1000 kg 1 g = 1 x 106 µg 1 g = 1 x 109 ng Volume SI Unit: cubic meter (m3) = kL 1 m3 = 1kL 1 L = 1.0567 qt 1 gal = 4 qt 1 dm3 = 1L 3.7854 L = 1 gal 1 qt = 2 pt 1 cm3 = 1 mL 1 pt = 2 cups 1 L = 1000 mL 1 cup = 8 oz 1 L = 1 x 106 µL 1 kL = 1000 L Time SI Unit: second (s) Temperature SI Unit: kelvin (K) 1 min = 60 sec 0 K = -273.15 oC 1 hr = 60 min K = oC + 273.15 1 day = 24 hr o C = 5/9(oF - 32) 1 yr = 365.25 day o F = 9/5(oC) + 32 Energy SI Unit: Joule (J) Pressure SI Unit: pascal (Pa) 1 J = 1 kg. m2/s2 1 atm = 101.325 kPa 1 cal = 4.184 J 1 atm = 760 mm Hg (or Torr) 1 J = 9.4781 x 10-4 btu 1 atm = 14.70 psi * btu = British Thermal Unit  Some Key Constants Gas Law Constant : R = 8.3145 J/K. mol Speed of Light: c = 2.9979 x 108 m/s Planck’s Constant: h = 6.626 x 10-34 J. s Avogadro’s number: N = 6.022 x 1023 atoms or molecules/ 1 mole Standard Temperature and Pressure (STP) = 273 K (0 oC) and 1 atm Mass of an electron: me = 9.109 x 10-31 kg Mass of a proton: mp = 1.673 x 10-27 kg Mass of a neutron: mn = 1.675 x 10-27 kg [Figure 1] Have you ever played golf, like the person in this photo? Even if you haven’t played golf before, you probably know that the goal of the game is to hit the ball into a hole with the fewest strokes of the club. Golf is a good way to understand two important concepts in scientific measurement: accuracy and precision. Accuracy The accuracy of a measurement is how close the measurement is to the true value. If you were to hit four different golf balls toward an over- sized hole, all of them might land in the hole. These shots would all be accurate because they all landed in the hole. This is illustrated in the sketch below. [Figure 2] Precision As you can see from the sketch above, the four golf balls did not land as close to one another as they could have. Each one landed in a different part of the hole. Therefore, these shots are not very precise. The precision of measurements is how close they are to each other. If you make the same measurement twice, the answers are precise if they are the same or at least very close to one another. The golf balls in the sketch below landed quite close together in a cluster, so they would be considered precise. However, they are all far from the hole, so they are not accurate. [Figure 3] Q: If you were to hit four golf balls toward a hole and your shots were both accurate and precise, where would the balls land? A: All four golf balls would land in the hole (accurate) and also very close to one another (precise). Summary Accuracy means making measurements that are close to the true value. Precision means making measurements that are close in value to each other but not necessarily close to the true value. Review Complete this statement: A measurement is accurate when it is __________. What makes two measurements precise? Kami measured the volume of a liquid three times and got these results: 66.71 mL, 66.70 mL, 66.69 mL. The actual volume of the liquid is 69.70 mL. Are Kami’s measurements precise? Are they accurate? Explain your answers. Resources 1.25 Scientific Measuring Devices FlexBooks 2.0 > Physical Science > Scientific Measuring Devices Last Modified: Apr 19, 2019 [Figure 1] The device pictured above is called a pH meter. It is a scientific measuring device that measures the acidity of a liquid. Being able to use scientific measuring devices such as this is an important science skill. That’s because doing science typically involves making many measurements. For example, if you do lab exercises in science, you might measure an object’s length or mass, or you might find the volume of a liquid. Scientists use sensitive measuring devices to make measurements such as these. The measurements are usually made using SI units of measurement. Measuring Length with a Metric Ruler You’ve probably been using a ruler to measure length since you were in elementary school. But you may have made most of the measurements in English units of length, such as inches and feet. In science, length is most often measured in SI units, such as millimeters and centimeters. Many rulers have both types of units, one on each edge. The ruler pictured below has only SI units. It is shown here bigger than it really is so it’s easier to see the small lines, which measure millimeters. The large lines and numbers stand for centimeters. Count the number of small lines from the left end of the ruler (0.0). You should count 10 lines because there are 10 millimeters in a centimeter. [Figure 2] Q: What is the length in millimeters of the red line above the metric ruler? A: The length of the red line is 32 mm. Q: What is the length of the red line in centimeters? A: The length of the red line is 3.2 cm. Measuring Mass with a Balance Mass is the amount of matter in an object. Scientists often measure mass with a balance. A type of balance called a triple beam balance is pictured in Figure below. To use this type of balance, follow these steps: Place the object to be measured on the pan at the left side of the balance. Slide the movable masses to the right until the right end of the arm is level with the balance mark. Start by moving the larger masses and then fine tune the measurement by moving the smaller masses as needed. Read the three scales to determine the values of the masses that were moved to the right. Their combined mass is equal to the mass of the object. [Figure 3] The Figure below is an enlarged version of the scales of the triple beam balance in Figure above. It allows you to read the scales. The middle scale, which measures the largest movable mass, reads 300 grams. This is followed by the top scale, which reads 30 grams. The bottom scale reads 5.1 grams. Therefore, the mass of the object in the pan is 335.1 grams (300 grams + 30 grams + 5.1 grams). [Figure 4] Q: What is the maximum mass this triple beam balance can measure? A: The maximum mass it can measure is 610 grams (500 grams + 100 grams + 10 grams). Q: What is the smallest mass this triple beam balance can measure? A: The smallest mass it can measure is one-tenth (0.1) of a gram. To measure very small masses, scientists use electronic balances, like the one in the Figure below. This type of balance also makes it easier to make accurate measurements because mass is shown as a digital readout. In the picture, the balance is being used to measure the mass of a white powder on a plastic weighing tray. The mass of the tray alone would have to be measured first and then subtracted from the mass of the tray and powder together. The difference between the two masses is the mass of the powder alone. [Figure 5] Measuring Volume with a Graduated Cylinder At home, you might measure the volume of a liquid with a measuring cup. In science, the volume of a liquid might be measured with a graduated cylinder, like the one sketched below. The cylinder in the picture has a scale in milliliters (mL), with a maximum volume of 100 mL. Follow these steps when using a graduated cylinder to measure the volume of a liquid: Place the cylinder on a level surface before adding the liquid. After adding the liquid, move so your eyes are at the same level as the top of the liquid in the cylinder. Read the mark on the glass that is at the lowest point of the curved surface of the liquid. This is called the meniscus. [Figure 6] Q: What is the volume of the liquid in the graduated cylinder pictured above? A: The volume of the liquid is 67 mL. Q: What would the measurement be if you read the highest point of the curved surface of the liquid by mistake? A: The measurement would be 68 mL. Resources 1.24 International System of Units (SI) FlexBooks 2.0 > Physical Science > International System of Units (SI) Last Modified: Aug 17, 2018 [Figure 1] In 1999, NASA’s Mars Climate Orbiter, pictured here, burned up as it passed through Mars’ atmosphere. The satellite was programmed to orbit Mars at high altitude and gather climate data. Instead, the Orbiter flew too low and entered the red planet’s atmosphere. Why did the Orbiter fly off course? The answer is human error. The flight system software on the Orbiter was written using scientific units of measurement, but the ground crew was entering data using common English units. SI Units The example of the Mars Climate Orbiter shows the importance of using a standard system of measurement in science and technology. The measurement system used by most scientists and engineers is the International System of Units, or SI. There are a total of seven basic SI units, including units for length (meter) and mass (kilogram). SI units are easy to use because they are based on the number 10. Basic units are multiplied or divided by powers of ten to arrive at bigger or smaller units. Prefixes are added to the names of the units to indicate the powers of ten, as shown in the Table below. Prefixes of SI Units Prefix Multiply Basic Unit × Basic Unit of Length = Meter (m) kilo- (k) 1000 kilometer (km) = 1000 m deci- (d) 0.1 decimeter (dm) = 0.1 m centi- (c) 0.01 centimeter (cm) = 0.01 m milli- (m) 0.001 millimeter (mm) = 0.001 m micro- (µ) 0.000001 micrometer (µm) = 0.000001 m nano- (n) 0.000000001 nanometer (nm) = 0.000000001 m Q: What is the name of the unit that is one-hundredth (0.01) of a meter? A: The name of this unit is the centimeter. Q: What fraction of a meter is a decimeter? A: A decimeter is one-tenth (0.1) of a meter. Unit Conversions In the Table below, two basic SI units are compared with their English system equivalents. You can use the information in the table to convert SI units to English units or vice versa. For example, from the table you know that 1 meter equals 39.37 inches. How many inches are there in 3 meters? 3 m = 3(39.37 in) = 118.11 in Unit Conversions Measure SI Unit English Unit Equivalent Length meter (m) 1 m = 39.37 in Mass kilogram (kg) 1 kg = 2.20 lb Q: Rod needs to buy a meter of wire for a science experiment, but the wire is sold only by the yard. If he buys a yard of wire, will he have enough? (Hint: There are 36 inches in a yard.) A: Rod needs 39.37 inches (a meter) of wire, but a yard is only 36 inches, so if he buys a yard of wire he won’t have enough. Summary The measurement system used by most scientists and engineers is the International System of Units, or SI. There are seven basic SI units, including units for length and mass. If you know the English equivalents of SI units, you can convert SI units to English units or vice versa. Review What does SI stand for? Why is it important for scientists and engineers to adopt a common system of measurement units? How many grams equal 1 kilogram? What fraction of a meter is a millimeter? How many pounds equal 5 kilograms? Resources