Question

The atomic mass of copper is 63.55 amu. What would be the mass of 75 copper atoms? How many copper atoms are contained in a sample of copper that has a mass of 6100.8 amu?

Short answer

The mass of 75 copper atoms is 4766.25 amu, and the number of copper atoms in the 6100.8 amu sample is 96.

Step-by-step solution

Calculate the mass of 75 copper atoms

To find the mass of 75 copper atoms, we'll multiply the atomic mass of copper by the number of atoms: \(Mass\; of\; 75\; copper\; atoms = Atomic\; mass\; of\; copper * 75\) Plug in the given values: \(Mass\; of\; 75\; copper\; atoms = 63.55\; amu * 75\)

Calculate the result

Multiply 63.55 amu by 75 to determine the mass of 75 copper atoms: \(Mass\; of\; 75\; copper\; atoms = 4766.25\; amu\)

Calculate the number of copper atoms in the sample

To find the number of copper atoms in the sample with mass 6100.8 amu, we'll use the following formula: \(Number\; of\; copper\; atoms = \frac{Mass\; of\; the\; sample}{Atomic\; mass\; of\; copper}\) Plug in the given values: \(Number\; of\; copper\; atoms = \frac{6100.8\; amu}{63.55\; amu}\)

Calculate the result

Divide 6100.8 amu by 63.55 amu to find the number of copper atoms in the sample: \(Number\; of\; copper\; atoms = 96\) Therefore, the mass of 75 copper atoms is 4766.25 amu, and the number of copper atoms in the 6100.8 amu sample is 96.

Key concepts

Atomic Mass Unit

Understanding the atomic mass unit (amu) is fundamental in the realm of chemistry and chemical calculations. An atomic mass unit is defined as a unit of mass equal to one-twelfth of the mass of a carbon-12 atom, which is approximately equal to 1.66053906660 x 10^-24 grams. This tiny unit allows chemists to compare the masses of different atoms on a relative scale. In practical terms, the atomic mass of an element, expressed in amu, corresponds to the average mass of the element's isotopes as they occur naturally, weighted by their abundances.

For example, copper’s atomic mass is stated as 63.55 amu, representing the average mass of copper's isotopes. When performing calculations, such as determining the mass of a specific number of atoms, we use the atomic mass as a conversion factor. This is because one mole of any element, defined as Avogadro’s number of atoms (approximately 6.022 x 10²³), will have a mass in grams that is equal to the element’s atomic mass in amu.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is essential for predictive purposes, allowing chemists to calculate the amounts of substances consumed and produced in a reaction.

Using stoichiometry, scientists can figure out the amount of a reactant needed to produce a specific quantity of product, or conversely, how much product can be made from a given amount of reactant. The stoichiometric coefficients in a balanced chemical equation give the ratios in which molecules react and are formed. This pivotal concept also applies to atomic level calculations such as figuring out how many atoms are in a given sample, or how much mass a certain number of atoms will have, as shown in the exercise provided.

Chemical Calculations

Chemical calculations are integral in translating theoretical chemistry into practical applications. These calculations use the principles of stoichiometry and other chemical properties to interpret and predict the outcomes of chemical processes. When engaging in chemical calculations, one often deals with the mole concept and molar masses to bridge the gap between the micro (atomic or molecular) scale and the macro (grams, liters, etc.) scale.

For instance, the exercise illustrates a basic chemical calculation involving atomic mass and number of atoms. In the solution, to find the mass of 75 copper atoms, the atomic mass (given in amu per atom) is multiplied by the number of atoms. This kind of calculation is fundamental to understanding larger stoichiometric problems. For more complex chemical calculations, one might employ limiting reactant concepts, percentage yield calculations, and concentration measures such as molarity, each of which contributes to the full understanding of quantitative aspects in chemistry.