There are approximately 0.75 gram atoms present in 103 grams of barium. This value is derived by relating the given mass of barium to its specific molar mass.
Understanding Gram Atoms
The term "gram atom" is a historical unit that is equivalent to a mole of atoms. A mole represents a specific quantity of a substance containing Avogadro's number of particles (approximately 6.022 × 10²³). For an element, one gram atom (or one mole of atoms) is the amount whose mass in grams is numerically equal to its atomic weight (or molar mass) expressed in grams per mole (g/mol).
For elements like barium (Ba), which are unimolecular (meaning they naturally exist as individual atoms rather than molecules), the molar mass directly corresponds to the mass of one gram atom.
Molar Mass of Barium
Barium (Ba) is an alkaline earth metal. Its molar mass is approximately 137.4 grams per mole (g/mol). This value is a fundamental property of the element, typically found on the periodic table.
Calculation of Gram Atoms
To determine the number of gram atoms in a given mass of an element, you use the following formula:
$$ \text{Number of Gram Atoms} = \frac{\text{Mass of Substance (g)}}{\text{Molar Mass (g/mol)}} $$
Using the provided information for barium:
- Mass of Barium: 103 g
- Molar Mass of Barium: 137.4 g/mol
Let's apply these values to the formula:
$$ \text{Number of Gram Atoms} = \frac{103 \text{ g}}{137.4 \text{ g/mol}} $$
Performing the calculation:
$$ \text{Number of Gram Atoms} \approx 0.7496 \text{ mol} $$
Rounding this to two decimal places, we find that there are approximately 0.75 gram atoms of barium in 103 grams.
Summary of Calculation
For clarity, here's a quick reference table outlining the values and the result:
| Property | Value | Unit |
|---|---|---|
| Mass of Barium | 103 | grams (g) |
| Molar Mass of Barium | 137.4 | g/mol |
| Gram Atoms (Result) | (103 g / 137.4 g/mol) $\approx$ 0.75 | gram atoms (mol) |
Practical Insights
Understanding how to convert between mass and gram atoms (or moles) is a cornerstone of chemistry. This skill is crucial for:
- Stoichiometry: Determining the exact quantities of reactants and products in chemical reactions.
- Solution Preparation: Calculating the precise amount of solute needed for a desired concentration.
- Quantitative Analysis: Measuring and analyzing the composition of substances.
By accurately performing these conversions, chemists can ensure the efficiency and safety of various processes in laboratories and industries.
