f(z)=8z^2-18z+7 Evaluate f(9) and solve f(z)=33 Explain please, if possible.?

2019-02-27 3:21 pm
Calculate the mass of caffeine (C8H10N4O2) that will contain 3.517 x 1023 N atoms

回答 (1)

2019-02-27 4:44 pm
f(z) = 8z² - 18z + 7

f(9) = 8×9² - 18×9 + 7
f(9) = 648 - 162 + 7
f(9) = 493

====
f(z) = 33
8z² - 18z + 7 = 33
8z² - 18z - 26 = 0
4z² - 9z - 13 = 0
(4z - 13)(z + 1) = 0
4z - 13 = 0 or z + 1 = 0
z = 13/4 or z = -1

====
Avogadro constant = 6.022 × 10²³ /mol
Moles of N atoms = (3.517 ×10²³) / (6.022 × 10²³ /mol) = 0.5840 mol

Each mole of C₈H₁₀N₄O₂ contains 4 moles of N atoms.
Moles of C₈H₁₀N₄O₂ = (0.5840 mol) / 4 = 0.1460

Molar mass of C₈H₁₀N₄O₂ = (12.01×8 + 1.008×10 + 14.01×4 + 16.00×2) g/mol = 194.20 g/mol
Mass of C₈H₁₀N₄O₂ = (0.1460 mol) × (194.20 g/mol) = 28.4 g

OR:
(3.517 ×10²³ N atom) × (1 mol N atoms /6.022 × 10²³ N atoms) × (1 mol C₈H₁₀N₄O₂ / 4 mol N atoms) × (194.2 g C₈H₁₀N₄O₂ / 1 mol C₈H₁₀N₄O₂)
= 28.4 g C₈H₁₀N₄O₂


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