Chapter 5: Problem 6
In a chemical formula, how do you calculate the number of atoms of an element within parentheses? Provide an example.
Short Answer
Expert verified
Multiply the subscript of each element within the parentheses by the subscript outside the parentheses. In \( Ca(NO_3)_2 \), there is 1 Ca, 2 N, and 6 O atoms.
Step by step solution
01
Identifying Elements within Parentheses
First, identify the formula units or elements that are within parentheses. These parentheses indicate that the elements inside are grouped together and should be treated as a single unit.
02
Recognizing the Subscript Outside the Parentheses
Look for the subscript number immediately following the closing parenthesis. This subscript indicates how many times the entire group within the parentheses will be counted.
03
Calculating the Total Number of Atoms for Each Element
To find the total number of each type of atom, multiply the subscript inside the parentheses by the subscript outside the parentheses. Do this for each element inside the parentheses.
04
Example Calculation
Consider the chemical formula \( Ca(NO_3)_2 \). The group \( NO_3 \) is within parentheses and has a subscript of 2 outside the parentheses. The formula therefore contains 1 atom of calcium (Ca), \( 2 \times 1 = 2 \) atoms of nitrogen (N), and \( 2 \times 3 = 6 \) atoms of oxygen (O).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Calculating Atoms in Chemical Formulas
Understanding how to calculate the number of atoms in chemical formulas is a fundamental aspect of chemistry that allows us to determine the precise make-up of compounds. To begin this calculation, one must scrutinize the chemical formula and pinpoint each element present. After identification, the next step is to count the number of atoms for each element.
For elements not enclosed by parentheses, simply look at the subscript following the element symbol which represents the number of atoms of that element. If there's no subscript, it's implied that there is only one atom of that element. However, when an element is inside parentheses, this indicates the element is part of a polyatomic ion or a repeating unit within the compound.
To compute the total number of atoms for an element within parentheses, multiply the subscript inside by the subscript outside. This operation is often visualized as distributing the outside subscript to each element within the parentheses. If an element inside the parentheses does not have its own subscript, treat it as having a subscript of one. This approach ensures that students can accurately dissect the molecular structure and appreciate the frequency of each constituent atom.
For elements not enclosed by parentheses, simply look at the subscript following the element symbol which represents the number of atoms of that element. If there's no subscript, it's implied that there is only one atom of that element. However, when an element is inside parentheses, this indicates the element is part of a polyatomic ion or a repeating unit within the compound.
To compute the total number of atoms for an element within parentheses, multiply the subscript inside by the subscript outside. This operation is often visualized as distributing the outside subscript to each element within the parentheses. If an element inside the parentheses does not have its own subscript, treat it as having a subscript of one. This approach ensures that students can accurately dissect the molecular structure and appreciate the frequency of each constituent atom.
Chemical Formula Subscripts
The small numbers you see immediately following element symbols in a chemical formula are known as subscripts. These subscripts are pivotal because they indicate the number of atoms of each element present in the smallest unit of the chemical compound.
For instance, in a water molecule represented by the chemical formula H2O, the subscript '2' after hydrogen (H) tells us that there are two hydrogen atoms for every one oxygen atom, as emphasized by the absence of a subscript after the oxygen (O).
When chemicals are combined with others to form a compound, as is the case with polyatomic ions, parentheses are employed to encapsulate them, and the subscript outside the parentheses applies to all elements within. Remember, when there’s no subscript outside the parentheses, it implies one unit of the group is involved, mirroring the convention used with individual element symbols.
For instance, in a water molecule represented by the chemical formula H2O, the subscript '2' after hydrogen (H) tells us that there are two hydrogen atoms for every one oxygen atom, as emphasized by the absence of a subscript after the oxygen (O).
When chemicals are combined with others to form a compound, as is the case with polyatomic ions, parentheses are employed to encapsulate them, and the subscript outside the parentheses applies to all elements within. Remember, when there’s no subscript outside the parentheses, it implies one unit of the group is involved, mirroring the convention used with individual element symbols.
Molecular Composition Analysis
Molecular composition analysis requires a thorough examination of the molecular formula to understand the compound's structure. When given a molecular formula, one can not only count atoms but also deduce the ratio of atoms, infer the molecular mass, and understand the spatial arrangement of atoms within the molecule.
An intrinsic part of this analysis involves understanding the significance of subscripts and superscripts. Delving deeper, isotopic composition or the presence of various isotopes of an element can also be deduced if the molecular formula includes isotopic notation. A complete molecular composition analysis provides insights into the properties of the compound, such as reactivity, phase of matter under certain conditions, and its role in chemical reactions.
To master the analysis, it's critical for students to be comfortable with reading and interpreting chemical formulas—a skill that is polished by plenty of practice, starting with recognizing atomic constituents to predicting intermolecular interactions based on molecular composition.
An intrinsic part of this analysis involves understanding the significance of subscripts and superscripts. Delving deeper, isotopic composition or the presence of various isotopes of an element can also be deduced if the molecular formula includes isotopic notation. A complete molecular composition analysis provides insights into the properties of the compound, such as reactivity, phase of matter under certain conditions, and its role in chemical reactions.
To master the analysis, it's critical for students to be comfortable with reading and interpreting chemical formulas—a skill that is polished by plenty of practice, starting with recognizing atomic constituents to predicting intermolecular interactions based on molecular composition.