Dimethylnitrosamine, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{N}_{2} \mathrm{O}$ is a carcinogenic (cancer causing) substance that may be formed in foods, beverages, or gastric juices from the reaction of nitrite ion (used as a food preservative) with other substances. a. What is the molar mass of dimethylnitrosamine? b. How many moles of $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{N}_{2} \mathrm{O}$ molecules are present in 250 mg dimethylnitrosamine? c. What is the mass of 0.050 mole of dimethylnitrosamine? d. How many atoms of hydrogen are in 1.0 mole of dimethylnitrosamine? e. What is the mass of \(1.0 \times 10^{6}\) molecules of dimethylnitrosamine? f. What is the mass in grams of one molecule of dimethylnitrosamine?

Step by step solution

01

Find the molar mass of individual elements

We need to find the molar mass of C, H, N, and O. - Carbon (C): 12.01 g/mol - Hydrogen (H): 1.01 g/mol - Nitrogen (N): 14.01 g/mol - Oxygen (O): 16.00 g/mol

02

Determine the molar mass of dimethylnitrosamine

Using the molar masses of the individual elements, we can find the molar mass of the whole compound. Molar mass of \((\mathrm{CH}_{3})_{2} \mathrm{N}_{2} \mathrm{O}\) = \([(2 × 12.01) + (6 × 1.01) + (2 × 14.01) + 16.00] \,\mathrm{g/mol}\) = \(74.16 \,\mathrm{g/mol}\) b. Calculate the number of moles in 250 mg of dimethylnitrosamine.

03

Convert mass to moles

To convert the mass of dimethylnitrosamine to moles, we will use the molar mass we found earlier (74.16 g/mol). No. of moles = \(\frac{250 \,\mathrm{mg}}{74.16 \,\mathrm{g/mol}}\) = \(\frac{0.250 \,\mathrm{g}}{74.16 \,\mathrm{g/mol}}\) = \(3.37 \times 10^{-3}\) moles c. Calculate the mass of 0.050 mole of dimethylnitrosamine.

04

Convert moles to mass

We can use the molar mass we found earlier and multiply it by the number of moles given to find the mass. Mass = No. of moles × Molar mass = \(0.050 \,\mathrm{mol} \times 74.16 \,\mathrm{g/mol}\) = \(3.71 \,\mathrm{g}\) d. Find the number of hydrogen atoms in 1.0 mole of dimethylnitrosamine.

05

Determine the number of H atoms per molecule

There are 2 CH3 groups per molecule, with each group containing 3 H atoms. So, the total number of H atoms per molecule is 2 × 3 = 6.

06

Calculate the total number of H atoms in 1.0 mole

Now, multiply the number of H atoms per molecule by Avogadro's number (6.022 × 10^23) to find the total number of hydrogen atoms in 1.0 mole of dimethylnitrosamine. No. of H atoms = 6 × 1.0 mole × 6.022 × 10^23 = \(3.61 \times 10^{24}\) H atoms e. Calculate the mass of \(1.0 \times 10^{6}\) molecules of dimethylnitrosamine.

07

Convert number of molecules to moles

First, find the number of moles using Avogadro's number. No. of moles = \(\frac{1.0 \times 10^{6}}{6.022 \times 10^{23}}\) = \(1.66 \times 10^{-18}\) moles

08

Calculate the mass

We can now use the molar mass to find the mass of \(1.0 \times 10^{6}\) molecules. Mass = No. of moles × Molar mass = \(1.66 \times 10^{-18} \,\mathrm{mol} \times 74.16 \,\mathrm{g/mol}\) = \(1.23 \times 10^{-16} \,\mathrm{g}\) f. Find the mass of one molecule of dimethylnitrosamine.

09

Calculate the mass of one molecule

The mass of one molecule can be found by dividing the mass of \(1.0 \times 10^6\) molecules by \(1.0 \times 10^6\). Mass of one molecule = \(\frac{1.23 \times 10^{-16} \,\mathrm{g}}{1.0 \times 10^{6}}\) = \(1.23 \times 10^{-22} \,\mathrm{g}\)

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