If 4.61 * 10^21 atoms of element Z have a mass of 0.815 g, what is the identity of Z?

Verified step by step guidance

Step 1: Calculate the number of moles of element Z using Avogadro's number. Avogadro's number is approximately 6.022 x 10^23 atoms/mol. Use the formula: \( \text{moles of Z} = \frac{\text{number of atoms}}{\text{Avogadro's number}} \).

Step 2: Substitute the given number of atoms (4.61 x 10^21) into the formula to find the moles of Z.

Step 3: Calculate the molar mass of element Z using the mass given (0.815 g) and the moles calculated in Step 2. Use the formula: \( \text{molar mass} = \frac{\text{mass}}{\text{moles}} \).

Step 4: Substitute the values from Step 2 and the given mass into the formula to find the molar mass of Z.

Step 5: Compare the calculated molar mass to known molar masses of elements on the periodic table to identify element Z.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of atoms, molecules, or particles in one mole of a substance. This concept is crucial for converting between the number of atoms and the amount of substance in grams, allowing us to relate the microscopic scale of atoms to the macroscopic scale of grams.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for identifying elements based on their mass and the number of atoms present, as it allows us to calculate the mass of a given number of atoms and determine the identity of the element.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. In this context, it helps us understand how to use the number of atoms and their corresponding mass to find the identity of element Z by relating these quantities to its molar mass.

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