The principal component of many kidney stones is calcium oxalate, CaC₂O₄. A kidney stone recovered from a typical patient contains 8.5 × 10²⁰ formula units of calcium oxalate. How many moles of CaC₂O₄ are present in this kidney stone? What is the mass of the kidney stone in grams?

Verified step by step guidance

1. Step 1: Recall the relationship between formula units and moles. The number of formula units can be converted to moles using Avogadro's number, which is approximately 6.022 x 10^23 formula units per mole. The formula to use is: \( \text{moles} = \frac{\text{number of formula units}}{\text{Avogadro's number}} \).
2. Step 2: Substitute the given number of formula units (8.5 x 10^20) and Avogadro's number (6.022 x 10^23) into the formula. Perform the division to calculate the number of moles of calcium oxalate (CaC2O4).
3. Step 3: To find the mass of the kidney stone, recall the relationship between moles, molar mass, and mass: \( \text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \).
4. Step 4: Determine the molar mass of calcium oxalate (CaC2O4) by summing the atomic masses of its constituent elements: calcium (Ca, 40.08 g/mol), carbon (C, 12.01 g/mol), and oxygen (O, 16.00 g/mol). The molar mass is calculated as: \( 40.08 + (2 \times 12.01) + (4 \times 16.00) \).
5. Step 5: Multiply the number of moles of CaC2O4 (calculated in Step 2) by the molar mass of CaC2O4 (calculated in Step 4) to find the mass of the kidney stone in grams.

Key Concepts

Moles and Avogadro's Number

A mole is a unit in chemistry that represents 6.022 x 10^23 entities, such as atoms or molecules. This number, known as Avogadro's number, allows chemists to convert between the number of particles and the amount of substance in moles. To find the number of moles of calcium oxalate in the kidney stone, one would divide the total number of formula units by Avogadro's number.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For calcium oxalate (CaC2O4), the molar mass can be calculated by summing the atomic masses of its constituent elements: calcium (Ca), carbon (C), and oxygen (O). This value is essential for converting moles of a substance into grams, which is necessary to determine the mass of the kidney stone.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. It allows for the calculation of the amounts of substances involved in a reaction based on their molar ratios. In this context, stoichiometry is used to relate the number of moles of calcium oxalate to its mass, facilitating the conversion from moles to grams.