Potassium metal reacts with water to give potassium hydroxide and hydrogen gas. If 50.0 mL of hydrogen gas is produced at STP, what is the mass of potassium that reacted?
2K(s) + 2 H2O (l) -> 2 KOH (aq) + H2(g)
mols H2 gas = mL/22,400 = ?
Using the coefficients in the balanced equation, convert mols H2 gas to mols K.
Now convert mols K to grams. g = mols K x atomic mass K = ?
To find the mass of potassium (K) that reacted, we need to use stoichiometry and the molar ratio between potassium and hydrogen gas.
The balanced equation tells us that 2 moles of potassium (2K) react with 1 mole of hydrogen gas (H2). This means that the ratio of K to H2 is 2:1.
Given that 50.0 mL of hydrogen gas is produced, we need to convert this volume to moles using the ideal gas law at standard temperature and pressure (STP).
At STP, 1 mole of any ideal gas occupies a volume of 22.4 liters. Thus, 50.0 mL (or 0.05 liters) of hydrogen gas is equal to:
0.05 L / 22.4 L/mol = 0.0022321 moles of H2.
Since the ratio of K to H2 is 2:1, we know that half as many moles of potassium reacted. Therefore, the amount of potassium that reacted is 0.0022321 / 2 = 0.001116 moles.
To find the mass of potassium, we need to multiply the number of moles by its molar mass. The molar mass of potassium (K) is 39.10 g/mol.
Mass of potassium = 0.001116 moles × 39.10 g/mol = 0.0437 grams.
Therefore, the mass of potassium that reacted is approximately 0.0437 grams.
To determine the mass of potassium that reacted, we can use stoichiometry. Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction.
First, let's write down the balanced chemical equation:
2K(s) + 2H₂O(l) -> 2KOH(aq) + H₂(g)
According to the balanced equation, 2 moles of potassium react with 2 moles of water to produce 1 mole of hydrogen gas.
Since we know the volume of hydrogen gas produced (50.0 mL) at STP, we can use the ideal gas law to determine the number of moles of hydrogen gas. At STP (standard temperature and pressure conditions), 1 mole of any ideal gas occupies 22.4 liters.
Using the equation: (Volume of gas in liters) = (Number of moles of gas) * (Molar volume at STP),
we can convert the volume of hydrogen gas (50.0 mL) to liters:
50.0 mL * (1 L / 1000 mL) = 0.0500 L
Now, let's calculate the number of moles of hydrogen gas using the ideal gas law:
(Number of moles of gas) = (Volume of gas in liters) / (Molar volume at STP)
= 0.0500 L / 22.4 L/mol
≈ 0.00223 mol
According to the balanced chemical equation, 1 mole of hydrogen gas is formed from 2 moles of potassium. Therefore, we can calculate the number of moles of potassium:
(Number of moles of potassium) = (Number of moles of hydrogen gas) * (2 moles of potassium / 1 mole of hydrogen gas)
= 0.00223 mol * (2 mol K / 1 mol H₂)
= 0.00446 mol K
Now we can calculate the mass of potassium using its molar mass. The molar mass of potassium (K) is approximately 39.10 grams/mol.
(Mass of potassium) = (Number of moles of potassium) * (Molar mass of potassium)
= 0.00446 mol * 39.10 g/mol
≈ 0.1748 g
Therefore, the mass of potassium that reacted is approximately 0.1748 grams.