To find out how many atoms of hydrogen are in 564 grams of sodium glutamate (NaC₅H₈NO₄), we will go through the following steps:
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Calculate the molar mass of sodium glutamate (NaC₅H₈NO₄):
- Sodium (Na) = 22.99 g/mol
- Carbon (C) = 12.01 g/mol, and there are 5 carbons: 5 × 12.01 = 60.05 g/mol
- Hydrogen (H) = 1.01 g/mol, and there are 8 hydrogens: 8 × 1.01 = 8.08 g/mol
- Nitrogen (N) = 14.01 g/mol
- Oxygen (O) = 16.00 g/mol, and there are 4 oxygens: 4 × 16.00 = 64.00 g/mol
Now, add these together to get the molar mass: \[ \text{Molar mass} = 22.99 + 60.05 + 8.08 + 14.01 + 64.00 = 169.13 \text{ g/mol} \]
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Calculate the number of moles in 564 grams of sodium glutamate: We can find the number of moles (n) using the formula: \[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{564 \text{ g}}{169.13 \text{ g/mol}} \approx 3.34 \text{ moles} \]
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Calculate the number of hydrogen atoms: Each mole of sodium glutamate contains 8 moles of hydrogen atoms: \[ \text{Hydrogen atoms} = 3.34 \text{ moles} \times 8 \text{ atoms/mole} = 26.72 \text{ moles of H atoms} \]
Now, to find the total number of hydrogen atoms: \[ \text{Number of atoms} = 26.72 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \approx 1.61 \times 10^{25} \text{ atoms} \]
Therefore, the closest answer from the options provided is:
d) 1.6 x 10^25.