Question

How many moles of calcium (Ca) atoms are in \(77.4 \mathrm{~g}\) of Ca?

Short answer

There are approximately 1.93 moles of calcium in 77.4 g of Ca.

Step-by-step solution

Find the Atomic Mass of Calcium

The atomic mass of calcium (Ca) is found on the periodic table. It is approximately \(40.08 \, \text{g/mol}\). This value represents the mass of one mole of calcium atoms.

Apply the Formula to Find Moles

We use the formula: \[\text{Moles of Ca} = \frac{\text{Given mass of Ca}}{\text{Molar mass of Ca}}\]Given that the mass of calcium is \(77.4 \, \text{g}\) and the molar mass is \(40.08 \, \text{g/mol}\), substitute these values into the formula.

Calculate the Moles of Calcium

Substitute the values into the formula:\[\text{Moles of Ca} = \frac{77.4 \, \text{g}}{40.08 \, \text{g/mol}} \approx 1.93 \, \text{mol}\]This calculation gives us the number of moles of calcium in \(77.4 \, \text{g}\) of calcium.

Key concepts

Atomic Mass of Elements

Atomic mass is an important concept when dealing with chemical elements. It refers to the mass of a single atom, usually expressed in atomic mass units (amu). Calcium, like all elements, has a specific atomic mass that we can conveniently find in the periodic table. For calcium, this value is approximately 40.08 amu. This number tells us how heavy a single atom of calcium is compared to the mass of a carbon atom, which is the standard reference.

Understanding atomic mass is crucial as it provides the foundation for further calculations in chemistry, such as determining the molar mass of an element. By knowing the atomic mass, scientists can predict how much an atom weighs and calculate how many atoms are present in a given mass.

Understanding Molar Mass

Molar mass is a key concept in chemistry that links weight to the number of particles. It is defined as the mass of one mole of a substance. For elements, the molar mass (often measured in grams per mole) is numerically equal to its atomic mass. So, for calcium (Ca), the molar mass is 40.08 g/mol, meaning one mole of calcium atoms weighs 40.08 grams.

Since the molar mass provides a bridge between the mass of a sample and the amount in moles, it is essential for converting grams to moles or vice versa. This conversion is fundamental for solving many chemistry problems where calculating the amount of substance is necessary for understanding the reactions and properties involved.

Periodic Table as a Tool

The periodic table is a critical tool in chemistry, visualizing complete information about elements. It not only organizes elements based on atomic number but also provides detailed data such as atomic mass and chemical properties.
- **Atomic Mass Information**: Clearly shown under the symbol of each element, allowing for quick reference. - **Chemical Properties**: Position of elements can hint the reactivity and types of compounds they can form.

Using the periodic table, chemists can predict how elements will interact and find essential data for calculations, like determining molar mass and calculating moles of a given substance. For calcium, simply locating Ca on the table gives us its atomic mass, necessary for any calculations involving the element.

Foundations of Chemistry Calculations

Chemistry calculations involve converting between different measurement units and often require understanding of foundational concepts like moles, atomic mass, and molar mass. Here are the steps for calculating moles from mass:

• **Identify Essential Data**: Atomic or molar mass, usually found on the periodic table.
• **Use Conversion Formulas**: \ For instance, compute moles using the formula: \ \[ \text{Moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}} \]
• **Execute Calculations**: Perform the math to find the result, converting mass to moles as needed.

These steps allow chemists to convert from measurable mass on a balance scale to the number of atoms or molecules in a sample, illuminating the invisible world of atoms and how substances interact. For instance, knowing how many moles of calcium are in a 77.4 g sample helps understand its potential chemical reactions.