Question

You are given 0.10-g samples of \(\mathrm{K}, \mathrm{Mo}, \mathrm{Cr},\) and \(\mathrm{Al}\). List the samples in order of the amount (moles), from smallest to largest.

Short answer

Mo, Cr, K, Al (from smallest to largest in moles).

Step-by-step solution

Finding the Molar Mass of Each Element

First, we need to find the molar mass of each of the given elements: Potassium (K), Molybdenum (Mo), Chromium (Cr), and Aluminum (Al). Based on the periodic table, the molar masses are approximately: \( K = 39.1 \, \text{g/mol} \), \( Mo = 95.95 \, \text{g/mol} \), \( Cr = 51.996 \, \text{g/mol} \), and \( Al = 26.98 \, \text{g/mol} \).

Calculating the Number of Moles for Each Element

Next, we need to calculate the number of moles for each 0.10-g sample using the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \).- For \( K \): \( \frac{0.10 \, \text{g}}{39.1 \, \text{g/mol}} \approx 0.00256 \, \text{mol} \).- For \( Mo \): \( \frac{0.10 \, \text{g}}{95.95 \, \text{g/mol}} \approx 0.00104 \, \text{mol} \).- For \( Cr \): \( \frac{0.10 \, \text{g}}{51.996 \, \text{g/mol}} \approx 0.00192 \, \text{mol} \).- For \( Al \): \( \frac{0.10 \, \text{g}}{26.98 \, \text{g/mol}} \approx 0.00371 \, \text{mol} \).

Ordering the Elements by Moles

Now, arrange the calculated moles in ascending order:- Molybdenum (Mo): \( 0.00104 \, \text{mol} \)- Chromium (Cr): \( 0.00192 \, \text{mol} \)- Potassium (K): \( 0.00256 \, \text{mol} \)- Aluminum (Al): \( 0.00371 \, \text{mol} \)

Conclusion

Based on the calculations, the order from the smallest to largest amount of moles is: Molybdenum (Mo), Chromium (Cr), Potassium (K), Aluminum (Al).

Key concepts

Molar Mass

When studying chemistry, understanding molar mass is crucial. Molar mass is essentially the weight of one mole of a given substance. It is expressed in grams per mole (g/mol). Each element has a unique molar mass, which can be found using the periodic table. To calculate the moles of a substance, we divide the mass of the sample by its molar mass. This is key for converting between grams and moles, helping us understand how much of a substance is present.

For instance, if you have a 1-gram sample of an element and its molar mass is 10 g/mol, you'd have 0.1 moles of that element. Understanding molar mass allows us to relate the mass of atoms and molecules to amounts we can see and measure, which is fundamental in chemical equations.

Periodic Table

The periodic table is like a map for chemists. It organizes all known chemical elements based on their properties and atomic number. Each element has a unique position on the table, which tells us a lot of important information.

• Atomic Number: The number of protons in an element's nucleus.
• Chemical Symbol: A one or two-letter abbreviation of the element's name.
• Atomic Mass: Usually found under the symbol, used to calculate the molar mass.

The periodic table is essential because it helps us quickly find the molar mass of elements, aiding in the calculation of moles and balancing chemical equations with stoichiometry. This well-arranged tool is indispensable for anyone studying or working in scientific fields.

Chemical Elements

Chemical elements are pure substances consisting of only one type of atom. Each element has a unique set of properties that differentiate it from others. Elements are the basic building blocks of matter and are represented by chemical symbols, like Al for aluminum or Cr for chromium.

These elements can exist as single atoms, molecules, or ions and partake in chemical reactions to form compounds. Knowing about chemical elements is critical because it helps us predict how substances interact in nature and controlled environments alike. For students and scientists, mastering the properties of elements is fundamental for safely handling chemicals and understanding molecular interactions.

Stoichiometry

Stoichiometry is the heart of chemical equations, allowing scientists to predict the outcomes of reactions quantitatively. It involves calculations that relate the quantities of reactants and products in a chemical reaction.

• Mole Ratio: Using coefficients from balanced chemical equations to convert between moles of different substances.
• Mass-to-Mass Calculations: Converting given mass of one substance to another using molar mass.

By applying stoichiometry, one can determine the amount of each reactant needed to produce a desired amount of product. It ensures efficiency and safety in chemical processes, making it essential for both academic and professional chemistry settings.