Mole-volume conversion factors

A problemsolving flowchart showing the use of mole-mole, mole-mass, mole-volume, and mole-particle conversion factors. 

The problem now becomes, What volume of SO2 is produced by the reaction of 2.48 L O2, with both gases at the same temperature and pressure This makes the volume-conversion factor the same as the mole ratio from the equation. Plan and complete the problem. 

Strategy (1) Start by calculating the number of moles of Fe2+. Then (2) use the coefficients of the balanced equation to find the number of moles of Mn04. Finally, (3), use molarity as a conversion factor to find the volume of KMn04 solution. 

As pointed out in Chapter 3, a balanced equation can be used to relate moles or grams of substances taking part in a reaction. Where gases are involved, these relations can be ex tended to include volumes. To do this, we use the ideal gas law and the conversion factor approach described in Chapter 3. 

If you look at Figure 9-2, you can see that it isn t possible to convert directly between the mass of one substance and the mass of another substance. You must convert to moles and then use the mole-mole conversion factor before converting to the mass of a new substance. The same can be said for conversions from the particles or volume of one substance to that of another substance. The mole is always the intermediary you use for the conversion. 

Again, conversion factors are the way to approach these kinds of problems. Each problem features a certain volume of solution that contains a certain solute at a certain concentration. To begin each problem, convert your volume into liters — part (c) has already done this for you. Then rearrange the molarity formula to solve for moles ... 

Basis of units listed below is 22.4140 liters at 0°C and 1 atm for the volume of 1 g mole. All other values were calculated from conversion factors. 

Then use this molarity as a conversion factor to calculate the number of moles of solute in the stated volume of solution. The mass of solute is given and the number of moles of solute present is now known therefore, to find the molar mass of the solute, divide the mass by the amount. To avoid rounding errors, do the numerical calculation at the end. 

Molarity can be used as a conversion factor to relate a solution s volume to the number of moles of solute. If we know the molarity and volume of a solution, we can calculate the number of moles of solute. If we know the number of moles of solute and the molarity of the solution, we can find the solution s volume. Worked Examples 3.11 and 3.12 show how such calculations are done. 

FIGURE 3.5 A flow diagram summarizing the use of molarity as a conversion factor between moles and volume in stoichiometry calculations. 

The concentration of a substance in solution is usually expressed as molarity (M), defined as the number of moles of a substance (the solute) dissolved per liter of solution. A solution s molarity acts as a conversion factor between solution volume and number of moles of solute, making it possible to carry out stoichiometry calculations on solutions. Often, chemicals are stored as concentrated aqueous solutions that are diluted before use. When carrying out a dilution, only the volume is changed by adding solvent the amount of solute is unchanged. A solution s exact concentration can often be determined by titration. 

A 4.028 m solution of ethylene glycol in water contains 4.028 mol of ethylene glycol per kilogram of water. To find the solution s molarity, we need to find the number of moles of solute per volume (liter) of solution. The volume, in turn, can be found from the mass of the solution by using density as a conversion factor. 

Because virtually all stoichiometric calculations involve moles (abbreviated mol) of material, molarity is probably the most common concentration unit in chemistry. If we dissolved 1.0 mol of glucose in enough water to give a total volume of 1.0 L, we would obtain a 1.0 molar solution of glucose. Molarity is abbreviated with a capital M. Notice that, because molarity has units of moles per liter, molar concentrations are conversion factors between moles of material and liters of solution. 

The following are the conversion factors from standard volumes to moles ... 

The concentration of a solute depends on the quantities of both the solute and the solution (or solvent). Molarity is defined as the number of moles of solute per liter of solution. Molarity is calculated by dividing the number of moles of solute by the volume of the solution in liters, or alternatively, by dividing the number of millimoles of solute by the milliliters of solution. Because molarity is a ratio, it can be used as a conversion factor to change the volume of solution into the number of moles of solute, or vice versa. 

The concentration of a substance in a mixture or solution can be used as a conversion factor to relate the mass (or moles) of a component in a sample of the mixture to the sample volume, or to relate the mass (or molar) flow rate of a component of a continuous stream to the total volumetric flow rate of the stream. Consider, for example, a 0.02-molar solution of NaOH (i.e., a solution containing 0.02 mol NaOH/L) 5 L of this solution contains... 

When reactants are liquids, they are almost always measured by volume. So, to do calculations involving liquids, you add two more steps to the sequence of mass-mass problems—the conversions of volume to mass and of mass to volume. Five conversion factors—two densities, two molar masses, and a mole ratio—are needed for this type of calculation, as shown in Skills Toolkit 4. 

What conversion factor is used to convert from volume of a gas directly to moles... 

Remember from Chapter 11 that the most convenient unit for counting numbers of atoms or molecules is the mole. One mole contains 6.02 X 10 particles. The molar volume for a gas is the volume that one mole occupies at 0.00°C and 1.00 atm pressure. These conditions of temperature and pressure are known as standard temperature and pressure (STP). Avogadro showed experimentally that one mole of any gas will occupy a volume of 22.4 L at STP. The fact that this value is the same for all gases greatly simplifies many gas law calculations. Because the volume of one mole of a gas at STP is 22.4 L, you can use the following conversion factor to find the number of moles, the mass, and even the number of particles in a gas sample. 

Because conditions are already at STP, multiply the known number of moles by the conversion factor that relates liters to moles to solve for the unknown volume. 

For example, suppose you need to calculate the molarity of 100.0 mL of an aqueous solution containing 0.085 mole of dissolved potassium chloride (KCl). You would first convert the volume of the solution from milliliters to liters using the conversion factor 1 L = 1000 mL. 

Calculate the number of moles of NaOH contained in the volume of standard solution added. First, convert milliliters of NaOH to liters by multiplying the volume by a conversion factor that relates milliliters and liters. 

Most chemical reactions that occur on the earth s surface, whether in living organisms or among inorganic substances, take place in aqueous solution. Chemical reactions carried out between substances in solution obey the requirements of stoichiometry discussed in Chapter 2, in the sense that the conservation laws embodied in balanced chemical equations are always in force. But here we must apply these requirements in a slightly different way. Instead of a conversion between masses and number of moles, using the molar mass as a conversion factor, the conversion is now between solution volumes and number of moles, with the concentration as the conversion factor. 

Therefore, we need conversion factors that convert back and forth between volumes of solutions and moles of solute in those solutions. Molarity (abbreviated M), which is defined as moles of solute per liter of solution, provides such conversion factors. 

Because the answer we want, molarity, is a ratio of two units (moles of solute—in this case, Na3P04—per liter of solution), we start our unit analysis setup with a ratio of two units. Because we want amount of Na3P04 on the top when we are done, we start with 8.20 g Na3P04 on the top. Because we want volume of solution on the bottom when we are done, we start with 100.0 mL of solution on the bottom. To convert mass of Na3P04 to moles of Na3P04, we use the molar mass of Na3P04. We finish our conversion with a conversion factor that converts milliliters to liters. 

Conversion factors constructed from molarities can be used in stoichiometric calculations in very much the same way conversion factors from molar mass are used. When a substance is pure, its molar mass can be used to convert back and forth between the measurable property of mass and moles. When a substance is in solution, its molarity can be used to convert between the measurable property of volume of solution and moles of solute. 

We complete the problem by using the molatity of AgN03 to convett from moles of AgN03 to volume of AgN03 solution. The value 1.00 M AgN03 provides us with two possible conversion factors. Like any conversion factors, they can be used in the form you see here or inverted. 

The molarity of phosphoric acid provides the conversion factor that converts from volume of H3PO4 solution to moles of H3PO4, and the molarity of sodium hydroxide provides the conversion factor that converts from moles of NaOH to volume of NaOH solution. The conversion from moles of H3PO4 to moles of NaOH is made with the molar ratio that comes from the coefficients in the balanced equation for the reaction. 

Molarity can be used to convert from volume of solution to moles of solute. (It might be necessary to insert one or more additional conversion factors to convert from the given volume unit to liters or milliliters.)... 

There are several ways to convert between moles of a gaseous substance and its volume. One approach is to use as a conversion factor the molar volume at STP. STP stands for standard temperature and pressure. Standard temperature is 0 °C, or 273.15 K, standard pressure is 1 atm, or 101.325 kPa, or 760 mmHg. The molar volume, or... 

We can use as a conversion factor to convert from volume in liters of H2 to moles of H2. We use it in the inverted form, with liters (L) on the bottom, so that liters will be canceled out. 

Between this chapter and Chapter 10, we have now seen three different ways to convert between a measurable property and moles in equation stoichiometry problems. The different paths are summarized in Figure 13.10 in the sample study sheet on the next two pages. For pure liquids and solids, we can convert between mass and moles, using the molar mass as a conversion factor. For gases, we can convert between volume of gas and moles using the methods described above. For solutions, molarity provides a conversion factor that enables us to convert between moles of solute and volume of solution. Equation stoichiometry problems can contain any combination of two of these conversions, such as we see in Example 13.8. 

For a gas under conditions other than STP, the ideal gas equation can be used to convert volume to moles, or the universal gas constant, R, can be used as a conversion factor. 

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