General orrganic and biological chemistry structures off liffe 5th by karen timberlake08 worked examples

Sample Problem 8.1 Properties of Gases Identify the property of a gas that is described by each of the following: a increase the kinetic energy of gas particles b the force of the gas particles hitting the walls of the container c the space that is occupied by a gas Solution a temperature b pressure c volume Study Check 8.1 As more helium gas is added to a balloon, the number of grams of helium increases What property of a gas is described? Answer The mass, in grams, gives the amount of gas General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.2 Units of Pressure The oxygen in a tank in the hospital respiratory unit has a pressure of 4820 mmHg Calculate the pressure, in atmospheres, of the oxygen gas (see Table 8.2) Solution The equality atm = 760 mmHg can be written as two conversion factors: General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.2 Units of Pressure Continued Using the conversion factor that cancels mmHg and gives atm, we can set up the problem as Study Check 8.2 A tank of nitrous oxide (N2O) used as an anesthetic has a pressure of 48 psi What is that pressure in atmospheres (see Table 8.2)? Answer 3.3 atm General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.3 Calculating Volume When Pressure Changes When Whitney had her asthma attack, oxygen was delivered through a face mask The gauge on a 12-L tank of compressed oxygen reads 3800 mmHg How many liters would this same gas occupy at a pressure of 0.75 atm when temperature and amount of gas not change? Solution Step Organize the data in a table of initial and final conditions To match the units for the initial and final pressures, we can convert either atm to mmHg or mmHg to atm General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.3 Calculating Volume When Pressure Changes Continued We place the gas data using units of mmHg for pressure and liters for volume in a table (We could have both pressures in units of atm as well.) The properties that not change, which are temperature and amount of gas, are shown below the table We know that pressure decreases, and can predict that the volume increases Factors that remain constant: T and n Step Rearrange the gas law equation to solve for the unknown quantity For a PV relationship, we use Boyle’s law and solve for V2 by dividing both sides by P2 According to Boyle’s law, a decrease in the pressure will cause an increase in the volume when T and n remain constant General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.3 Calculating Volume When Pressure Changes Continued Step Substitute values into the gas law equation and calculate When we substitute in the values with pressures in units of mmHg or atm, the ratio of pressures (pressure factor) is greater than 1, which increases the volume as predicted in Step Study Check 8.3 In an underground natural gas reserve, a bubble of methane gas, CH4, has a volume of 45.0 mL at 1.60 atm What volume, in milliliters, will the gas bubble occupy when it reaches the surface where the atmospheric pressure is 744 mmHg, if there is no change in the temperature or amount of gas? Answer 73.5 mL General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.4 Calculating Volume When Temperature Changes Helium gas is used to inflate the abdomen during laparoscopic surgery A sample of helium gas has a volume of 5.40 L and a temperature of 15 °C What is the final volume, in liters, of the gas if the temperature has been increased to 42 °C at constant pressure and amount of gas? Solution Step Organize the data in a table of initial and final conditions The properties that change, which are the temperature and volume, are listed in the following table The properties that not change, which are pressure and amount of gas, are shown below the table When the temperature is given in degrees Celsius, it must be changed to kelvins Because we know the initial and final temperatures of the gas, we know that the temperature increases Thus, we can predict that the volume increases T1 = 15 °C + 273 = 288 K T2 = 42 °C + 273 = 315 K Factors that remain constant: P and n Step Rearrange the gas law equation to solve for the unknown quantity In this problem, we want to know the final volume (V2) when the temperature increases Using Charles’s law, we solve for V2 by multiplying both sides by T2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.4 Calculating Volume When Temperature Changes Continued Step Substitute values into the gas law equation and calculate From the table, we see that the temperature has increased Because temperature is directly related to volume, the volume must increase When we substitute in the values, we see that the ratio of the temperatures 1temperature factor2 is greater than 1, which increases the volume as predicted in Step Study Check 8.4 A mountain climber with a body temperature of 37 °C inhales 486 mL of air at a temperature of –8 °C What volume, in milliliters, will the air occupy in the lungs, if the pressure and amount of gas not change? Answer 569 mL General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.5 Calculating Pressure When Temperature Changes Home oxygen tanks, which provide an oxygen-rich environment, can be dangerous if they are heated, because they can explode Suppose an oxygen tank has a pressure of 120 atm at a room temperature of 25 °C If a fire in the room causes the temperature of the gas inside the oxygen tank to reach 402 °C, what will be its pressure in atmospheres? The oxygen tank may rupture if the pressure inside exceeds 180 atm Would you expect it to rupture? Solution Step Organize the data in a table of initial and final conditions We list the properties that change, which are the pressure and temperature, in a table The properties that not change, which are volume and amount of gas, are shown below the table The temperatures given in degrees Celsius must be changed to kelvins Because we know the initial and final temperatures of the gas, we know that the temperature increases Thus, we can predict that the pressure increases T1 = 25 °C + 273 = 298 K T2 = 402 °C + 273 = 675 K Factors that remain constant: V and n General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.5 Calculating Pressure When Temperature Changes Continued Step Rearrange the gas law equation to solve for the unknown quantity Using Gay-Lussac’s law, we can solve for P2 by multiplying both sides by T2 Step Substitute values into the gas law equation and calculate When we substitute in the values, we see that the ratio of the temperatures (temperature factor), is greater than 1, which increases pressure as predicted in Step Because the calculated pressure of 270 atm of the gas exceeds the limit of 180 atm, we would expect the oxygen tank to rupture General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.6 Using the Combined Gas Law Continued Study Check 8.6 A weather balloon is filled with 15.0 L of helium at a temperature of 25 °C and a pressure of 685 mmHg What is the pressure, in millimeters of mercury, of the helium in the balloon in the upper atmosphere when the temperature is –35 °C and the final volume becomes 34.0 L, if the amount of He does not change? Answer 241 mmHg General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.7 Calculating Volume for a Change in Moles A weather balloon with a volume of 44 L is filled with 2.0 moles of helium What is the final volume, in liters, if 3.0 moles of helium gas are added, to give a total of 5.0 moles of helium gas, if the pressure and temperature not change? Solution Step Organize the data in a table of initial and final conditions We list those properties that change, which are volume and amount (moles) of gas, in a table The properties that not change, which are pressure and temperature, are shown below the table Because there is an increase in the number of moles of gas, we can predict that the volume increases Factors that remain constant: P and T Step Rearrange the gas law equation to solve for the unknown quantity Using Avogadro’s law, we can solve for V2 by multiplying both sides by n2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.7 Calculating Volume for a Change in Moles Continued Step Substitute values into the gas law equation and calculate When we substitute in the values, we see that the ratio of the moles (mole factor) is greater than 1, which increases the volume as predicted in Step Study Check 8.7 A sample containing 8.00 g of oxygen gas has a volume of 5.00 L What is the final volume, in liters, after 4.00 g of oxygen gas is added to the 8.00 g of oxygen in the balloon, if the temperature and pressure not change? Answer 7.50 L General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.8 Using Molar Volume to Find Volume at STP What is the volume, in liters, of 64.0 g of O2 gas at STP? Solution Step State the given and needed quantities Step Write a plan to calculate the needed quantity The grams of O are converted to moles using molar mass Then a molar volume conversion factor is used to convert the number of moles to volume (L) Step Write the equalities and conversion factors including 22.4 L/mole at STP General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.8 Using Molar Volume to Find Volume at STP Continued Step Set up the problem with factors to cancel units Study Check 8.8 How many grams of N2(g) are in 5.6 L of N2(g) at STP? Answer 7.0 g of N2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.9 Using the Ideal Gas Law Dinitrogen oxide, N2O, which is used in dentistry, is an anesthetic also called laughing gas What is the pressure, in atmospheres, of 0.350 mole of N2O at 22 °C in a 5.00-L container? Solution Step State the given and needed quantities When three of the four quantities (P, V, n, and T) are known, we use the ideal gas law equation to solve for the unknown quantity It is helpful to organize the data in a table The temperature is converted from degrees Celsius to kelvins so that the units of V, n, and T match the unit of the gas constant R General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.9 Using the Ideal Gas Law Continued Step Rearrange the ideal gas law equation to solve for the needed quantity By dividing both sides of the ideal gas law equation by V, we solve for pressure, P Step Substitute the gas data into the equation and calculate the needed quantity Study Check 8.9 Chlorine gas, Cl2, is used to purify water How many moles of chlorine gas are in a 7.00-L tank if the gas has a pressure of 865 mmHg and a temperature of 24 °C? Answer 0.327 mole of Cl2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.10 Calculating Mass Using the Ideal Gas Law Butane, C4H10, is used as a fuel for camping stoves If you have 108 mL of butane gas at 715 mmHg and 25 °C , what is the mass, in grams, of butane? Solution Step State the given and needed quantities When three of the quantities (P, V, and T) are known, we use the ideal gas law equation to solve for the unknown quantity, moles (n) Because the pressure is given in mmHg, we will use R in mmHg The volume given in milliliters (mL) is converted to a volume in liters (L) The temperature is converted from degrees Celsius to kelvins General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.10 Calculating Mass Using the Ideal Gas Law Continued Step Rearrange the ideal gas law equation to solve for the needed quantity By dividing both sides of the ideal gas law equation by RT, we solve for moles, n Step Substitute the gas data into the equation and calculate the needed quantity Now we can convert the moles of butane to grams using its molar mass of 58.12 g/mole: General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.10 Calculating Mass Using the Ideal Gas Law Continued Study Check 8.10 What is the volume, in liters, of 1.20 g of carbon monoxide at °C if it has a pressure of 724 mmHg? Answer 1.04 L General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.11 Gases in Chemical Reactions Calcium carbonate, CaCO3, in antacids reacts with HCl in the stomach to reduce acid reflux How many liters of CO2 are produced at 752 mmHg and 24 °C from a 25.0-g sample of calcium carbonate? Solution Step State the given and needed quantities Step Write a plan to convert the given quantity to the needed moles General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.11 Gases in Chemical Reactions Continued Step Write the equalities and conversion factors for molar mass and mole–mole factors Step Set up the problem to calculate moles of needed quantity Step Convert the moles of needed quantity to mass or volume using the molar mass or the ideal gas law equation General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.11 Gases in Chemical Reactions Continued Study Check 8.11 If 12.8 g of aluminum reacts with HCl, how many liters of H2 would be formed at 715 mmHg and 19 °C? Answer 18.1 L of H2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.12 Partial Pressure of a Gas in a Mixture A heliox breathing mixture of oxygen and helium is prepared for a patient with COPD (chronic obstructive pulmonary disease) The gas mixture has a total pressure of 7.00 atm If the partial pressure of the oxygen in the tank is 1140 mmHg, what is the partial pressure, in atmospheres, of the helium in the breathing mixture? Solution Step Write the equation for the sum of the partial pressures Step Rearrange the equation to solve for the unknown pressure To solve for the partial pressure of helium (PHe), we rearrange the equation to give the following: Convert units to match General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc Sample Problem 8.12 Partial Pressure of a Gas in a Mixture Continued Step Substitute known pressures into the equation and calculate the unknown partial pressure Study Check 8.12 An anesthetic consists of a mixture of cyclopropane gas, C3H6, and oxygen gas, O2 If the mixture has a total pressure of 1.09 atm, and the partial pressure of the cyclopropane is 73 mmHg, what is the partial pressure, in millimeters of mercury, of the oxygen in the anesthetic? Answer 755 mmHg General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc ... increases Using Charles’s law, we solve for V2 by multiplying both sides by T2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc... quantity Using Avogadro’s law, we can solve for V2 by multiplying both sides by n2 General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education, Inc... air occupy in the lungs, if the pressure and amount of gas not change? Answer 569 mL General, Organic, and Biological Chemistry: Structures of Life, 5/e Karen C Timberlake © 2016 Pearson Education,