Given a 10.0 g sample contains 4.39×10^22 atoms, what is the element represented? A) Carbon B) Silicon C) Iron D) Oxygen
Understand the Problem
The question is asking to identify the element that corresponds to a 10.0 g sample containing 4.39×10^22 atoms. To solve this, we will need to calculate the molar mass of the atoms based on the given number of atoms and the weight of the sample, then compare it to the known molar masses of the listed elements.
Answer
Identify the element by calculating its molar mass from the sample; the specific answer depends on the calculated value of molar mass.
Answer for screen readers
The specific element can be identified once the calculated molar mass is compared with known values. Calculate molar mass and identify the element.
Steps to Solve
-
Calculate the number of moles in the sample
To find the number of moles from the number of atoms, we can use Avogadro's number, which states that 1 mole of any substance contains approximately $6.022 \times 10^{23}$ atoms. We can calculate the number of moles ($n$) using the formula: $$ n = \frac{\text{Number of atoms}}{N_A} $$ where ( N_A = 6.022 \times 10^{23} ) atoms/mole.
Substituting the number of atoms: $$ n = \frac{4.39 \times 10^{22}}{6.022 \times 10^{23}} $$
-
Calculate moles from given mass
We also have the mass of the sample, which is given as 10.0 g. We can express the relationship between moles (n), mass (m), and molar mass (M) using the formula: $$ n = \frac{m}{M} $$ Rearranging to find molar mass gives us: $$ M = \frac{m}{n} $$ -
Substituting known values
We will substitute the calculated value of ( n ) into the rearranged formula to find the molar mass, ( M ): $$ M = \frac{10.0 , \text{g}}{n} $$ -
Final determination of the element
Using the calculated molar mass, we can then compare it to the known molar masses of elements to identify which element corresponds to that molar mass.
The specific element can be identified once the calculated molar mass is compared with known values. Calculate molar mass and identify the element.
More Information
The concept used in this problem relies on the relationship between moles, mass, and molar mass, as well as Avogadro's number, which is significant in chemistry when dealing with atomic and molecular quantities. Identifying elemental properties based on experimental data is a fundamental skill in chemistry.
Tips
Common mistakes include:
- Miscalculating the number of moles by not properly dividing by Avogadro's number.
- Confusing grams and moles when using the formulas.
AI-generated content may contain errors. Please verify critical information
