find out number of moles and mass of methane which contains 3 grams of of carbon

To determine the number of moles and the mass of methane (CH₄) that contains 3 grams of carbon, we first need to understand the composition of methane and how to convert grams of carbon into moles and then into the mass of methane.

Understanding Methane's Composition

Methane is a simple hydrocarbon made up of one carbon atom and four hydrogen atoms. Its chemical formula is CH₄. The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is about 1.01 g/mol. Therefore, the molar mass of methane can be calculated as follows:

• Molar mass of CH₄ = 1 × (molar mass of C) + 4 × (molar mass of H)
• Molar mass of CH₄ = 1 × 12.01 g/mol + 4 × 1.01 g/mol = 12.01 g/mol + 4.04 g/mol = 16.05 g/mol

Calculating Moles of Carbon

Next, we need to find out how many moles of carbon are present in 3 grams. The formula to calculate the number of moles is:

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

Using this formula:

Number of moles of carbon = 3 g / 12.01 g/mol ≈ 0.2497 moles

Relating Moles of Carbon to Moles of Methane

Since one mole of methane contains one mole of carbon, the number of moles of methane will be the same as the number of moles of carbon. Therefore, we also have:

Number of moles of methane = 0.2497 moles

Calculating the Mass of Methane

Now, to find the mass of methane that corresponds to these moles, we can use the moles-to-mass conversion formula:

Mass (g) = number of moles × molar mass (g/mol)

Substituting the values we have:

Mass of methane = 0.2497 moles × 16.05 g/mol ≈ 4.01 grams

Summary of Results

In summary, if you have 3 grams of carbon, it corresponds to approximately 0.2497 moles of carbon, which is also the same number of moles of methane. The mass of methane that contains this amount of carbon is approximately 4.01 grams.

This process illustrates how to convert between mass and moles using the relationships defined by the chemical composition of substances. Understanding these conversions is essential in chemistry for stoichiometric calculations and reactions.