What is the mass of [tex]$1.8 \times 10^{24}$[/tex] molecules of [tex]$CO_2$[/tex]?
([tex]$1 mol CO_2=44.01 g$[/tex])
([tex]$1 mol CO_2=6.02 \times 10^{23}$[/tex] molecules)
[?] [tex]$g CO_2$[/tex]
Answer (2)
131.59 g
Explanation
Problem Analysis We are given the number of C O 2 molecules and asked to find the mass in grams. We also know that 1 mole of C O 2 has a mass of 44.01 g and contains 6.02 × 1 0 23 molecules.
Calculating Moles First, we need to find out how many moles of C O 2 are present in 1.8 × 1 0 24 molecules. We can use the following formula: m o l es = A v o g a d r o ′ s n u mb er n u mb er o f m o l ec u l es where Avogadro's number is 6.02 × 1 0 23 molecules/mol.
Moles of CO2 Plugging in the values, we get: m o l es = 6.02 × 1 0 23 1.8 × 1 0 24 = 2.99
Calculating Mass Now that we know the number of moles, we can calculate the mass of C O 2 using the formula: ma ss = m o l es × m o l a r ma ss where the molar mass of C O 2 is 44.01 g/mol.
Mass of CO2 Plugging in the values, we get: ma ss = 2.99 × 44.01 = 131.59 g
Final Answer Therefore, the mass of 1.8 × 1 0 24 molecules of C O 2 is approximately 131.59 g.
Examples
Imagine you're baking a cake and the recipe calls for a specific number of C O 2 molecules (which is a bit unusual, but bear with me!). Knowing the mass of that many molecules helps you relate the microscopic world of molecules to the macroscopic world of grams, which you can measure with a kitchen scale. This conversion is essential in chemistry for accurately measuring reactants and products in chemical reactions. Understanding the relationship between the number of molecules, moles, and mass allows for precise control over chemical processes, ensuring the desired outcome in various applications, from baking to industrial manufacturing.
The mass of 1.8 × 1 0 24 molecules of C O 2 is approximately 131.59 g. This is found by calculating the number of moles of C O 2 using Avogadro's number and then multiplying by the molar mass. These calculations help relate the microscopic number of molecules to grams in a practical way.
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