Problem 27 - Chemistry The Science in Context

Question

How many moles of carbon are there in \(500.0 \mathrm{g}\) of carbon?

Step-by-Step Solution

Answer

Answer: There are 41.6 moles of carbon in 500.0 grams of carbon.

Step 1: Find the molar mass of carbon

The molar mass of carbon (C) is approximately 12.01 grams per mole (g/mol). You can find this value on the periodic table or in a chemistry textbook.

Step 2: Calculate the number of moles

To calculate the number of moles, use the given mass of carbon and the molar mass of carbon in the formula: Number of moles (n) = mass of substance (g) / molar mass (g/mol) Therefore, we can find the number of moles of carbon in 500.0 g: Number of moles of carbon = \(\frac{500.0\mathrm{g}}{12.01 \mathrm{g/mol}}\)

Step 3: Simplify the calculation

Divide 500.0 by 12.01 to get the number of moles of carbon: Number of moles of carbon = \(41.633 \mathrm{mol}\) Since the given mass of carbon (500.0 g) contained 3 significant figures, we should round off our answer to 3 significant figures as well, as it reflects the degree of precision in our calculation: Number of moles of carbon = \(41.6 \mathrm{mol}\) (rounded to 3 significant figures) Thus, there are 41.6 moles of carbon in 500.0 g of carbon.

Key Concepts

Molar Mass

Understanding the molar mass is a key step in solving chemistry problems related to moles. Molar mass tells us the mass of one mole of a substance in grams, which equates to its molecular weight. You can find this value for any element or compound by checking the periodic table. For example, the molar mass of carbon, denoted as C, is approximately 12.01 g/mol. This means one mole of carbon atoms weighs 12.01 grams.

When solving problems, it is essential to know the molar mass because it acts as a conversion factor between grams and moles. Whenever you have a sample and need to determine the number of moles, you will rely on the molar mass using the formula:

• Number of moles = mass of substance (g) / molar mass (g/mol)

By deciding on the correct molar mass from the periodic table, you are paving the way for accurate and effective calculations.

Significant Figures

Significant figures are crucial for precision and accuracy in scientific calculations. They help communicate the degree of certainty in your measurements and results. When you measure something and report it with significant figures, it signifies how reliable your figures are.

• For example, the measurement 500.0 has four significant figures because the zeros are counted as significant when they fall between a non-zero number and decimal point.

The importance of significant figures becomes apparent during calculations. They guide you in rounding numbers appropriately to reflect the uncertainty of your measurements. Thus, after calculating the moles of carbon in the given problem, we round the answer 41.633 to 41.6, preserving the three significant figures corresponding to the initial measurement of 500.0 grams.

Keep in mind that accurately applying significant figures can prevent cumulative errors and ensure the communicative integrity of your scientific data.

Calculation of Moles

Calculating moles is a fundamental operation in chemistry that converts mass, in grams, to moles through the molar mass. The concept stems from Avogadro's number, which provides a Bridge between atoms/molecules and grams. Calculating moles helps chemists understand how much of a substance participates or results from a chemical reaction.

• To perform a calculation, use the formula: Number of moles = mass of the substance (g) / molar mass (g/mol).

In our scenario involving carbon, we have 500.0 grams of carbon. By dividing this mass by carbon's molar mass, 12.01 g/mol, you obtain the number of moles. Following through the calculation gives approximately 41.633 moles.

After computing moles, do not forget to round according to significant figures, concluding with the result being 41.6 moles. This calculation is especially vital as it allows for stoichiometric computations in chemical equations, facilitating the prediction of product or reactant quantities. Embracing these calculation steps will bolster your understanding of chemical processes immensely.