Chapter 4: Problem 148
calculate the percent weight of each element in magnesium chloride, \(\mathrm{MgCl}_{2}\).
Short Answer
Expert verified
In magnesium chloride (\(MgCl_2\)), the percent weight of each element is approximately \(25.53\%\) for magnesium and \(74.47\%\) for chlorine.
Step by step solution
01
Find the molar mass for each element
We will use the periodic table to find the atomic masses of magnesium (Mg) and chlorine (Cl):
- Magnesium (Mg) has an atomic mass of \(24.31 g/mol\)
- Chlorine (Cl) has an atomic mass of \(35.45 g/mol\)
Now we have the molar mass for each element.
02
Calculate the molar mass of magnesium chloride (\(MgCl_2\))
To find the molar mass of \(MgCl_2\), we need to add the molar mass of one magnesium atom and the molar masses of two chlorine atoms:
\(MM_{MgCl_2} = 1 \times 24.31 + 2 \times 35.45\)
\(MM_{MgCl_2} = 24.31 + 70.90 \)
\(MM_{MgCl_2} = 95.21g/mol\)
Now we have the molar mass of magnesium chloride.
03
Calculate the percent weight of each element
We will now find the percent weight for each element by dividing the molar mass of the element by the molar mass of \(MgCl_2\), then multiply by \(100\%\):
Percent weight of Magnesium (Mg):
\(\%Mg = \frac{MM_{Mg}}{MM_{MgCl_2}} \times 100\%\)
\(\%Mg = \frac{24.31}{95.21} \times 100\%\)
\(\%Mg \approx 25.53\% \)
Percent weight of Chlorine (Cl):
\(\%Cl = \frac{MM_{Cl_{2}}}{MM_{MgCl_2}} \times 100\%\)
\(\%Cl = \frac{70.90}{95.21} \times 100\%\)
\(\%Cl \approx 74.47\% \)
The percent weight of each element in magnesium chloride (\(MgCl_2\)) is approximately \(25.53\%\) for magnesium and \(74.47\%\) for chlorine.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molar Mass Calculation
To determine the molar mass of a compound, first locate the atomic masses of its constituent elements on the periodic table. These atomic masses are expressed in grams per mole (g/mol), which is a unit that allows us to count atoms by weighing them. For magnesium chloride (\( MgCl_2 \) ), its molar mass is calculated by adding the atomic mass of one magnesium atom to the combined atomic masses of two chlorine atoms.
- Magnesium (\( Mg \) ) has an atomic mass of \( 24.31 \, g/mol \) .
- Chlorine (\( Cl \) ) has an atomic mass of \( 35.45 \, g/mol \) .
Atomic Mass
Atomic mass, often expressed as a decimal, represents the average mass of an atom of an element, taking into account the naturally occurring isotopes and their abundances. In simple terms, it reflects the weight an atom would have if it were on its own.The atomic mass is crucial when calculating the molar mass of compounds like magnesium chloride (\( MgCl_2 \) ). Consider that:
- The atomic mass of magnesium (\( Mg \) ) is \( 24.31 \, g/mol \) .
- The atomic mass of chlorine (\( Cl \) ) is \( 35.45 \, g/mol \) .
Magnesium Chloride
Magnesium chloride (\( MgCl_2 \) ) is a chemical compound comprising one magnesium atom and two chlorine atoms. This compound is commonly used in a variety of applications, including de-icing roads and in pharmaceutical formulations.Understanding magnesium chloride's structure and composition is crucial in fields like chemistry and environmental science. The compound dissociates into magnesium (\( Mg^{2+} \) ) and chloride (\( Cl^{-} \) ) ions when dissolved in water, making it an excellent source of magnesium for chemical reactions or nutrition.On the molecular level, \( MgCl_2 \) weighs \( 95.21 \, g/mol \) as derived from its molar mass calculation:
- 1 Magnesium (\( Mg \) ) x \( 24.31 \, g/mol \)
- 2 Chlorines (\( Cl \) ) x \( 35.45 \, g/mol \)
Chemical Formula Interpretation
A chemical formula like \( MgCl_2 \) provides plenty of information at a glance. It indicates not only the types of atoms present but also the number of each atom in the molecule. This interpretation is key in understanding how compounds will interact in reactions and their percent composition. For \( MgCl_2 \) :
- The subscript '2' next to 'Cl' signifies there are two chlorine atoms per magnesium atom in the compound.
- No subscript after 'Mg' implies there is only one magnesium atom.