Subscripts, in formulas

The collection of atoms represented by a formula is called a formula unit. A chemical formula consists of symbols of element(s), often with subscripts that tell how many atoms of each element are present per formula unit. The subscript/oZ/ows the symbol of the element it multiplies. If no subscript is present, one atom of the element is indicated. Parentheses may be used in a formula to group bonded atoms together, and a subscript after the closing parenthesis tells how many of that group are present per formula unit. The following formulas illustrate the meanings of subscripts in formulas ... 

In CU2S, the two copper ions are balanced by one sulfide ion with a 2 charge the charge on each copper ion must be 1 +. In CuS, only one copper ion is present to balance the 2- charge on the sulfide ion the charge on the copper ion is 2 +. Note that the Roman numerals in the names of monatomic cations denote the charges on the ions. The Arabic numerals appearing as subscripts in formulas denote the number of atoms of that element present per formula unit. Either of these numbers can be used to deduce the other, but they are not the same ... 

I Roman numerals in names stand for charges, and subscripts in formulas represent numbers of atoms. 

Oxidation numbers are used in the Stock system for naming compounds. Positive oxidation numbers are denoted as Roman numerals in parentheses in the names of the compounds the numbers of atoms or ions can be deduced from the oxidation numbers. (In contrast, the subscripts in formulas give the numbers of atoms or ions, from which the oxidation numbers may be deduced.) (Section 16.2). 

Before we attempt to balance an equation, all substances must be represented by formulas that describe them as they exist. For instance, we must write H2 to represent diatomic hydrogen molecules—not H, which represents hydrogen atoms. Once the correct formulas are written, the subscripts in the formulas may not be changed. Different subscripts in formulas specify different compounds, so changing the formulas would mean that the equation would no longer describe the same reaction. 

Notice how these suggestions worked in the procedures illustrated in this section. Above all, remember that we should never change subscripts in formulas, because doing so would describe different substances. We only adjust the coefficients to balance the equation. 

Chemical formulas and chemical equations both have a quantitative significance in that the subscripts in formulas and the coefficients in equations represent precise quantities. The formula H2O indicates that a molecule of this substance (water) contains exactly two atoms of hydrogen and one atom of oxygen. Similarly, the coefficients in a balanced chemical equation indicate the relative quantities of reactants and products. But how do we relate the numbers of atoms or molecules to the amounts we measure in the laboratory Although we cannot directly count atoms or molecules, we can indirectly determine their numbers if we know their masses. Therefore, before we can pursue the quantitative aspects of chemical formulas and equations, we must examine the masses of atoms and molecules. 

Chemical formulas and chemical equations both have a quantitative significance Ihe subscripts in formulas and the coefficients in equations represent precise quantities. The formula H2O indicates lhat a molecule of this substance contains exactly two atoms of hydrogen and one atom of oxygen. Similarly, the balanced chemical equation for the combustion of propane—... 

As an aid for determining subscripts in formulas for ionic compounds, the positive and negative charges can be crossed over. Crossing over is a method of balancing the charges between ions in an ionic compound. 

This reaction is further illustrated in Figure 1.4. As you study the molecular models, consider carefully the effects associated with changing the subscripts in formulas and those associated with changing coefficients. Also, be patient. Balancing equations is a skill that takes practice, and any chemist will admit to it being sometimes extremely complex. 

Formula coefficients are equivalent to subscripts in a formula or function as multipliers of the subscripts. Subscripts are not fixed numbers. Some students indicate that 2SO2 means two atoms of S and two atoms of O and draw 3H2 as a series of six linearly linked hydrogen atoms. They also balance a reaction equation by changing subscripts in formulas of reactants or products instead of coefficients. 

Strategy To find the molecular formulas, simply add up the atoms of each type and use the sums as subscripts in the formulas. 

The calculations in Example 3.4 illustrate an important characteristic of formulas. In one mole of Fe203 there are two moles of Fe (111.7 g) and three moles of O (48.00 g). This is the same as the atom ratio in Fe203,2 atoms Fe 3 atoms O. In general, the subscripts in a formula represent not only the atom ratio in which the different dements are combined but also the mole ratio. 

Equations are balanced by adjusting coefficients in front of formulas, never by changing subscripts within formulas. On paper, the equation discussed above could have been balanced by writing N6 on the right, but that would have been absurd. Elemental nitrogen exists as diatomic molecules, N2 there is no such thing as an N6 molecule. 

The ratios of subscripts in the formula can be determined if the elemental composition of an organism growing under particular conditions is known. A unique cell formula can then be established by relating elemental composition to one gram-atom of carbon, ie 9 = 1, then a, p, and 8 are set so that the formula is consistent with known relative elemental weight content of the cells. The formula can be extended to include other macro-elements, such as phosphate and sulphur, if elemental analysis shows these elements to be a significant proportion of cell material. 

An equation must never be balanced by changing the subscripts in the chemical formulas. That change would imply that different substances were taking part in the reaction. For example, changing H20 to H202 in the skeletal equation and writing... 

We have written the difference equation (14) at a fixed node x = x. With an arbitrarily chosen node it is plain to derive equation (14) at all inner nodes of the grid. Since at all the nodes x, i = 1, 2,.. ., IV — 1, the coefficients a, and are specified by the same formulae (15), scheme (14)-(15) is treated as a homogeneous conservative scheme. Because of this, we may omit the subscript i in formulae (14)-(15) and write down an alternative form of scheme (14) ... 

The chemical formula for water shows how formulas are constructed. The formula lists the symbols of all elements found in the compound, in this case H (hydrogen) and O (oxygen). A subscript number after an element s symbol denotes how many atoms of that element are present in the molecule. The subscript 2 in the formula for water indicates that each molecule contains two hydrogen atoms. No subscript is used when only one atom is present, as is the case for the oxygen atom in a water molecule. Atoms are indivisible, so molecules always contain whole numbers of atoms. Consequently, the subscripts in chemical formulas of molecular substances are always integers. We explore chemical formulas in greater detail in Chapter 3. 

In the problem above, we determined the percentage data from the chemical formula. We can determine the empirical formula if we know the percent compositions of the various elements. The empirical formula tells us what elements are present in the compound and the simplest whole-number ratio of elements. The data may be in terms of percentage, or mass or even moles. However, the procedure is still the same—convert each element to moles, divide each by the smallest, and then use an appropriate multiplier if necessary. We can then determine the empirical formula mass. If we know the actual molecular mass, dividing the molecular formula mass by the empirical formula mass, gives an integer (rounded if needed) that we can multiply each of the subscripts in the empirical formula. This gives the molecular (actual) formula, which tells what elements are in the compound and the actual number of each. 

In balancing chemical equations don t change the subscripts in the chemical formula, just the coefficients. 

Dividing the gram molecular mass you were given (194.2 g/mol) by this empirical formula mass yields the quotient, 2. Multiplying each of the subscripts in the empirical formula by 2 produces the molecular formula, CgHjgN 02. The common name for this culturally important compound is caffeine. 

Occasionally, you may be asked to calculate the mole fraction of a solution, which is the ratio of the number of moles of either solute or solvent in a solution to the total number of moles of solute and solvent in the solution. By the time chemists defined this quantity, however, they had finally acknowledged that they had too many m variables, and they gave it the variable X. Of course, chemists still need to distinguish between the mole fractions of the solute and the solvent, which unfortunately both start with the letter s. To avoid further confusion, they decided to abbreviate solute and solvent as A and B, respectively, in the general formula, although in practice, the chemical formulas of the solute and solvent eire usually written as subscripts in place of A and B. For example, the mole fraction of sodium chloride in a solution would be written as... 

Why is it important never to change a subscript in a chemical formula when balancing a chemical equation ... 

W hen a formula contains subscripts — the small numerals that indicate how many of a kind — be certain to multiply the atomic weight by the number indicated by the subscript. In cases where, the formula is preceded by a large number, be sure to multiply the molecular weight by this number.)... 

The molecular weight of the compound can be obtained from the molecular formula by summing the products obtained by multiplication of the atomic weights of Ihe elements limes their subscripts in the molecular formula. The latter contains all the information that the empirical formula contains bill in addition specifies the number of atoms in the molecule and also the molecular weight of the substance. 

Knowing a compound s percent composition makes it possible to calculate the compound s chemical formula. As shown in Figure 3.8, the strategy is to find the relative number of moles of each element in the compound and then use the numbers to establish the mole ratios of the elements. The mole ratios, in turn, give the subscripts in the chemical formula. 

Then multiply the subscripts in the empirical formula by this multiple to obtain the molecular formula. In our example, the molecular formula of octane is C(4x2)H(9x2)/ or CgH18. 

The empirical formula mass (88.0 amu) is half the molecular mass of ascorbic acid (176 amu), so the subscripts in the empirical formula must be multiplied by 2 ... 

Note that the subscripts in a molecular formula represent the number of atoms in a molecule. Since a molecule of CuS04 has four oxygen atoms, the relative mass of oxygen must be multiplied by four and added to the relative mass of one copper atom and one sulfur atom to find the relative mass of a mole of CuS04, copper sulfate molecules. Two atoms of potassium, four atoms of oxygen, and one atom of chromium must be accounted for in potassium chromate, K2Cr04. Students should calculate the mass of one mole of each of the molecules needed, convert each to 0.1 mole (multiply by... 

The law of conservation of matter states that in a closed system when a chemical change occurs, there is no change in mass. This is because atoms are conserved in a chemical change so atoms must be balanced in a chemical equation. In a balanced equation, coefficients tell the number of reactant and product substances that react and are produced. Subscripts tell the number of atoms of each kind in these substances. When a coefficient is multiplied by a subscript in a substance formula, the number of atoms is determined. Since a mole is an amount of a substance, the coefficients in a chemical equation can stand for the number of moles that react and are produced. 

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