Question

The meat from one hazelnut has a mass of \(0.985 \mathrm{~g}\). (a) What is the mass of a millionth of a mole \(\left(10^{-6}\right)\) of hazelnut meats? (A millionth of a mole is also called a micromole.) (b) How many moles are in a pound of hazelnut meats?

Short answer

Answer: The mass of a micromole of hazelnut meats is \(970 \times 10^{-9}\, \text{g}\), and there are approximately \(460.9\, \text{mol}\) of hazelnut meats in a pound.

Step-by-step solution

(Part a: Find the mass of a micromole of hazelnut meats)

We follow these steps to find the mass of a micromole of hazelnut meats: 1. Determine the moles of one hazelnut meat (\(n_\text{meat}\)), given that one hazelnut has a mass of \(0.985 \mathrm{~g}\). 2. Divide the number of moles of one hazelnut meat (\(n_\text{meat}\)) by a million to get the moles for a micromole. 3. Multiply the moles of a micromole by the mass of one hazelnut meat to determine the mass of a micromole of hazelnut meats. First, we calculate the moles of one hazelnut meat (\(n_\text{meat}\)) by dividing the mass of one hazelnut meat by its molar mass: $$n_\text{meat} = \frac{m_\text{meat}}{M_\text{meat}}$$ We need the molar mass of hazelnut meat, but it's not provided. In this case, we assume that the mass of a hazelnut corresponds to one unit, so the molar mass is 1 g/mol. $$n_\text{meat} = \frac{0.985 \mathrm{~g}}{1} = 0.985\, \text{mol}$$ Now, we find the moles of a micromole by dividing the moles of one hazelnut meat by a million: $$n_\text{micromole} = \frac{n_\text{meat}}{10^6} = \frac{0.985\, \text{mol}}{10^6} = 9.85\times10^{-7}\, \text{mol}$$ Finally, we determine the mass of a micromole of hazelnut meats: $$m_\text{micromole} = n_\text{micromole} \cdot m_\text{meat} = 9.85\times10^{-7}\, \text{mol} \cdot 0.985 \mathrm{~g} = 970\times10^{-9}\, \text{g}$$ Thus, the mass of a micromole of hazelnut meats is \(970 \times 10^{-9}\, \text{g}\).

(Part b: Calculate the number of moles in a pound of hazelnut meats)

First, we need to convert the mass of a pound of hazelnut meats to grams. There are 454 grams in a pound. So, the mass of a pound of hazelnut meats is: $$m_\text{pound} = 1\, \text{lb} \cdot \frac{454\, \text{g}}{1\,\text{lb}} = 454\, \text{g}$$ Now, we calculate the number of moles in a pound of hazelnut meats by dividing the mass of a pound of hazelnut meats by the mass of one hazelnut meat: $$n_\text{pound} = \frac{m_\text{pound}}{m_\text{meat}} = \frac{454\, \text{g}}{0.985 \mathrm{~g}} \approx 460.9\, \text{mol}$$ Thus, there are approximately \(460.9\, \text{mol}\) of hazelnut meats in a pound.