Understanding the Gram Molecular Mass of Sucrose: Key Concepts and Calculations

Understanding the gram molecular mass of sucrose is a fundamental concept in chemistry, particularly when dealing with solutions and reactions. In this article, we will delve into the process of calculating the gram molecular mass (or molar mass) of sucrose and explore related concepts such as moles and Avogadro's number.

Introduction to Gram Molecular Mass and Molar Mass

The gram molecular mass or molar mass of a substance is the mass in grams of one mole (Avogadro's number) of that substance. For sucrose (Sucrose: C12H22O11), its molar mass is a crucial value for chemical calculations and stoichiometric problems. Avogadro's number, NA 6.022 times; 1023, represents the number of atoms or molecules in one mole of a substance.

Step-by-Step Calculation of Molar Mass

To calculate the molar mass of sucrose, we need to consider the contributions of each element in the molecule's formula (C12H22O11). The atomic weights of each constituent element are as follows:

Carbon (C): 12.01 g/mol Hydrogen (H): 1.01 g/mol Oxygen (O): 16.00 g/mol

Let's break it down step-by-step:

Carbon (C): There are 12 carbon atoms in sucrose. Hydrogen (H): There are 22 hydrogen atoms in sucrose. Oxygen (O): There are 11 oxygen atoms in sucrose.

Now, we multiply the number of each element by its atomic weight:

12 C atoms: (12 times 12.01 144.12) g/mol 22 H atoms: (22 times 1.01 22.22) g/mol 11 O atoms: (11 times 16.00 176.00) g/mol

Next, we sum these values:

Molar mass of sucrose 144.12 22.22 176.00 342.34 g/mol

Thus, the gram molecular mass of sucrose is approximately 342.34 g/mol.

The Importance of Moles and Avogadro's Number

To further clarify the concept, let's consider the mass of 0.105 moles of sucrose. Using the molar mass we just calculated:

Mass of 0.105 moles 0.105 mol times; 342.296 g/mol 35.9 grams of sucrose.

We can also calculate the mass of a single molecule of sucrose:

Molecular mass of sucrose (in grams per molecule) (frac{342.3 , text{g/mol}}{6.022 times 10^{23} , text{molecules/mol}})

Which gives us:

Mass of one sucrose molecule 56.84 times; 10-23 grams per molecule

This calculation is essential for understanding the molecular composition and behavior of sucrose in various chemical processes.

Conclusion

Understanding the gram molecular mass of sucrose and its molar mass is crucial for chemical calculations and stoichiometric problems. By breaking down the composition of a molecule and using Avogadro's number, we can determine the mass of a specific number of molecules or moles of any compound. This knowledge is fundamental for a wide range of applications in chemistry and related fields.