Final answer:
To calculate the grams of sodium metal needed to produce 7.81 g of hydrogen by the reaction between sodium metal and water, we can use the mole ratio from the balanced equation. First, convert the mass of hydrogen to moles, then use the mole ratio to find the moles of sodium, and finally convert the moles of sodium to grams.
Step-by-step explanation:
The reaction between sodium metal and water can be represented by the equation:
2Na (s) + 2H₂O (l) → 2NaOH (aq) + H₂ (g)
From the balanced equation, we can see that for every 2 moles of sodium, we get 1 mole of hydrogen. To calculate the grams of sodium metal needed to produce 7.81 g of hydrogen, we need to convert the grams of hydrogen to moles and then use the mole ratio from the balanced equation to find the moles of sodium. Finally, we can convert the moles of sodium to grams.
First, we calculate the moles of hydrogen:
moles of hydrogen = mass of hydrogen (g) / molar mass of hydrogen (g/mol)
moles of hydrogen = 7.81 g / 2.02 g/mol = 3.87 mol
Next, we use the mole ratio from the balanced equation to find the moles of sodium:
moles of sodium = (moles of hydrogen) / (moles of hydrogen per mole of sodium)
moles of sodium = 3.87 mol / 1 mol = 3.87 mol
Finally, we convert the moles of sodium to grams:
grams of sodium = moles of sodium × molar mass of sodium
grams of sodium = 3.87 mol × 22.99 g/mol = 88.9 g