Calculate the mass (in g) of each sample. a. 4.5×10 25 O 3 molecules

Hello, everyone to deal with the following problem, calculate the mass in grams of the sample. So we have 4.5 times 10 to the 25 moles of ox zone of ozone. And so what we need to do is we need to take our given which is our 4.5 times 10 to the 25th ozone molecules. And we need to first convert this into a known ratio in that we can multiply this by the mole to molecules ratio or just avocado's number that states than in one mole over ozone. There are 6.022 times 10 to the 23rd molecules. When our units of molecules of ozone cancel out, we are left with 75 moles of ozone. But we're not done yet. Recall that one oxygen atom has a molar mass of 16 g per mole. So ozone will have a molar mass of 48 g per mole. Let's calculate the number of moles to the mass. And we can do that by saying that the mass will be equal to the number of moles times our molar mass. So we have, our mass is equal to the number of moles, which we calculated was 75 moles of ozone. And then we have that ratio with the molar mass, that one mole of ozone is equal to 48 grams of our ozone. When our units of moles of ozone cancel out, we are left with 3600 g of ozone as our final answer or answer choice C and with that, we have solved the problem overall, I hope this helped and until next time.

Ch.3 - Molecules and Compounds

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Tro 6th Edition

Ch.3 - Molecules and Compounds

Problem 76a

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Chapter 3, Problem 76a

Calculate the mass (in g) of each sample. a. 4.5×10²⁵ O₃ molecules

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Determine the number of moles of O3 molecules using Avogadro's number. Avogadro's number is approximately 6.022 \times 10^{23} molecules per mole. Use the formula: \text{moles} = \frac{\text{number of molecules}}{\text{Avogadro's number}}.

Calculate the molar mass of O3. Oxygen (O) has an atomic mass of approximately 16 g/mol. Since O3 consists of three oxygen atoms, multiply the atomic mass of oxygen by three.

Use the molar mass of O3 and the number of moles calculated in step 1 to find the mass. Apply the formula: \text{mass} = \text{moles} \times \text{molar mass}.

Ensure the units are consistent throughout the calculation. The final mass should be in grams (g).

Double-check your calculations for any possible errors to ensure accuracy.

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Key Concepts

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

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For ozone (O3), the molar mass can be calculated by summing the atomic masses of its constituent atoms: three oxygen atoms. This value is essential for converting between the number of molecules and mass.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances to the microscopic scale, enabling calculations involving the number of molecules and moles.

Conversion from Molecules to Grams

To convert the number of molecules to grams, one must first determine the number of moles by dividing the number of molecules by Avogadro's number. Then, multiply the number of moles by the molar mass of the substance. This two-step process is crucial for accurately calculating the mass of a sample based on its molecular count.