Tools for problem solving:
Q: A new baby weighs 7.8 lb. What is the mass in Kg?
A: 3.5 Kg (2.205 lb= 1Kg.)
Q: A piece of lumber is 88.4 cm long. What is its length in mm and in inches?
A: 884mm and 34.8 in. (know 1 in.=2.54 cm)
Q: A bottle of soda contains 2.0 L. What is the volume in quarts? (1L=1.06 qt.)
A: 2.12 qt.
Q: In the Olympics, there is a 100 m fly event. How long is the race in feet? In yards?
A: 328 ft.
Q: How many seconds are in 1 day?
A: 86,400 s
Q: Your car has a 5.00 L engine. What is the size of your engine in cubic inches?
A: 305 cubic inches
Density:
Q: A block has a volume of 25.3 cubic centimeters. Its mass is 21.7 g. Calculate the density of the block.
A: 0.858 g/cm3
Q: A Student fills a graduated cylinder to 25mL with liquid. She then immerses a solid in the liquid. The volume of the liquid rises to 33.9 mL. The mass of the solid is 63.5g. what is the density of the solid?
A: 7.1g/mL
Q: Isopropyl alcohol has a density of 0.785 g/mL. What volume should be measured to obtain 20.0 g of the liquid?
A: 25.5 mL
Q: A student needs 150 cubic centimeters of salt for an experiment. The density of salt is 2.16 g/mL. How many one pound boxes of salt should he buy at the grocery store?
A: 324g. he needs 1 box
Q: A beaker contains 725mL of water. The density of water is 1g/mL. What is the volume of the water in liters and what is the mass of the water.
A: 0.725 L, 725g
Atomic Masses: Counting atoms by weighing:
Q: Calculate the mass in amu of a sample of carbon that contains 62 atoms.
A: 744.6 amu
Q: Calculate the mass, in amu, of a sample of iron that contains 15 atoms.
A: 837.8 amu
Q: Calculate the number of copper atoms present in a sample that has a mass of 1779.4 amu.
A: 28.00 atoms
Q: Calculate the number of Ar atoms present in a sample that has a mass of 3755.3 amu.
A: 94.00 atoms
The mole:
Q: Calculate the number of moles of atoms and the number of atoms in a 25.0 g sample of calcium.
A: 0.624 mol Ca; 3.76 x 1023 Ca atoms.
Q: Calculate the number of moles of atoms and the number of atoms in a 57.7 g sample of sulfur.
A: 1.80 mol S; 1.08 x 1024 S atoms.
Q: Calculate the # of atoms in a 23.6 mg sample of Zn.
A: 2.17 x 1020 Zn atoms
Q: Calculate the number of atoms in a 128.3 mg sample of silver.
A: 7.16 x 1020 Ag atoms.
Molar Mass:
Q: Calculate the mass of 1.48 mol of potassium oxide
A: 139 g potassium oxide
Q: Calculate the mass of 4.85 mol of acetic acid.
A: 291 g
Q: Formaldehyde, which in the past was used to preserve biological samples, has the formula H2CO. How many moles of formaldehyde does a 7.55 g sample represent?
A: 0.251 mol formaldehyde
Q: How many moles of tetraphosphorus decoxide does a 250.0 g sample represent?
A: 0.8805 mol tetraphosphorus decoxide.
Q: How many water molecules are in a 10.0 g sample of H2O?
A: 3.34 x 1023 water molecules
Q: How many molecules of sucrose are in a 5.00 lb bag of sugar?
A: 3.99 x 1024 sugar molecules
Percent composition of compounds:
Q: Determine the mass percent of each element in sulfuric acid
A: 2.055% hydrogen; 13.42% sulfur; 65.25% oxygen
Q: Determine the mass percent of each element in isopropyl alcohol.
A: 59.96% carbon; 13.42% hydrogen; 26.62% oxygen
Empirical Formulas:
Q: Determine the empirical formula from each of the following molecular formulas.
1. H2O2, hydrogen peroxide, a substance commonly diluted as water and used as a disinfectant.
2. C4H10, butane, commonly used in lighters
3. CCl4, carbon tetrachloride, an organic solvent.
Calculation of Empirical formulas:
Q: a 1.500 g sample of a compound containing only carbon and hydrogen is found to contain 1.198 g of carbon. Determine the empirical formula for thiscompound.
A: CH3
Q: A 3.450 g sample of nitrogen reacts with 1.970 g of oxygen. Determine the empirical formula for this compound.
A: N2O
Q: When a 2.000 g sample of iron metal is heated in air, it reacts with oxygen to achieve a final mass of 2.573 g. Determine the empirical formula for this iron oxide.
A: Iron (II) oxide
Q: A 4.550 g sample of cobalt reacts with 5.475 g chlorine to form a binary compound. Determine the empirical formula for this compound.
A: CoCl2
Q: Phosphoric acid is found in some soft drinks. A sample of phosphoric acid contains 0.3086 g of hydrogen, 3.161 g phosphorus, and 6.531 g oxygen. Determine the empirical formula of phosphoric acid.
A: H3PO4
Q: Para-dichlorobenzene is often used in chemistry labs when studying melting points. A sample of p-dichlorobenzene contains 5.657 g carbon, 0.3165 g hydrogen, and 5.566 g chlorine. Determine the empirical formula.
A: C3H2Cl
Calculation of Molecular formulas:
Q: A compound containing carbon, hydrogen, and oxygen is found to be 40.00% carbon and is 6.700% hydrogen. The molar mass of the compound is between 115 g/mol and 125 g/mol. Determine the molecular formula for this compound.
A: C4H8O4
Q: Caffeine is a compound containing carbon, hydrogen, nitrogen, and oxygen. The mass percent composition of caffeine is 49.47% carbon, 5.191% hydrogen, 28.86 nitrogen, and 15.48% oxygen. The molar mass of caffeine is approximately 194 g/mol. Determine the molecular formula for caffeine.
A: C8H10N4O2
Another Problem:
Vitamin C contains three elements: carbon, hydrogen, and oxygen. Analysis of pure vitamin C indicates that the elements are present in the following mass percentages:
C = 40.9
H = 4.58
O = 54.5
Use the data to determine the simplest formula for vitamin C.
Solution
We want to find the number of moles of each element in order to determine the ratios of the elements and the formula. To make the calculation easy (i.e., let the percentages convert directly to grams), let's assume we have 100 g of vitamin C. If you are given mass percentages, always work with a hypothetical 100 gram sample. In a 100 gram sample, there are 40.9 g C, 4.58 g H, and 54.5 g O. Now, look up the atomic masses for the elements from the Periodic Table. The atomic masses are found to be:
H is 1.01
C is 12.01
O is 16.00
The atomic masses provide a moles per gram conversion factor. Using the conversion factor, we can calculate the moles of each element:
moles C = 40.9 g C x 1 mol C / 12.01 g C = 3.41 mol C
moles H = 4.58 g H x 1 mol H / 1.01 g H = 4.53 mol H
moles O = 54.5 g O x 1 mol O / 16.00 g O = 3.41 mol O
The numbers of moles of each element are in the same ratio as the number of atoms C, H, and O in vitamin C. To find the simplest whole number ratio, divide each number by the smallest number of moles:
C: 3.41 / 3.41 = 1.00
H: 4.53 / 3.41 = 1.33
O: 3.41 / 3.41 = 1.00
The ratios indicate that for every one carbon atom there is one oxygen atom. Also, there are 1.33 = 4/3 hydrogen atoms. (Note: converting the decimal to a fraction is a matter of practice! You know the elements must be present in whole number ratios, so look for common fractions and become familiar with the decimal equivalents for fractions so you can recognize them.) Another way to express the atom ratio is to write it as 1 C : 4/3 H : 1 O. Multiply by three to obtain the smallest whole-number ratio, which is 3 C: 4 H : 3 O. Thus, the simplest formula of vitamin C is C3H4O3.