If 15.00 g of solid zinc reacts with 100.0 mL of 4.00 M hydrochloric acid, what volume of hydrogen gas is produced at 25°C and 1.00 atm?
To determine the volume of hydrogen gas produced, we first need to calculate the number of moles of zinc and hydrochloric acid that react.
Step 1: Calculate moles of zinc (Zn)
The molar mass of zinc (Zn) is 65.38 g/mol.
Moles of Zn = (mass of Zn) / (molar mass of Zn)
Moles of Zn = 15.00 g / 65.38 g/mol
Moles of Zn = 0.2292 mol
Step 2: Calculate moles of hydrochloric acid (HCl)
The concentration of hydrochloric acid (HCl) is given as 4.00 M, which means there are 4.00 moles of HCl dissolved in 1 liter (1000 mL) of solution.
Moles of HCl = (concentration of HCl) x (volume of HCl)
Moles of HCl = 4.00 mol/L x (100.0 mL / 1000 mL/L)
Moles of HCl = 0.400 mol
Step 3: Determine the limiting reactant
To determine the limiting reactant, we compare the moles of zinc (0.2292 mol) and hydrochloric acid (0.400 mol).
Since the ratio of Zn to HCl is 1:2 (according to the balanced chemical equation below), we need twice as many moles of hydrochloric acid to react with all the zinc.
Zn + 2HCl -> ZnCl2 + H2
Since we have less moles of zinc than hydrochloric acid, zinc is the limiting reactant.
Step 4: Calculate moles of hydrogen gas (H2)
According to the balanced chemical equation, 1 mole of zinc produces 1 mole of hydrogen gas:
Zn + 2HCl -> ZnCl2 + H2
Therefore, the moles of hydrogen gas produced will be equal to the moles of zinc.
Moles of H2 = moles of Zn = 0.2292 mol
Step 5: Calculate volume of hydrogen gas at STP
Standard temperature and pressure (STP) is defined as 0°C (273 K) and 1 atm. To convert the moles of hydrogen gas to a volume at STP, we'll use the ideal gas law.
PV = nRT
Where:
P = pressure (1 atm)
V = volume of gas at STP (in liters, which we need to calculate)
n = moles of gas (0.2292 mol)
R = gas constant (0.0821 L x atm/(mol x K))
T = temperature (25°C + 273 K = 298 K)
Plugging the values into the ideal gas law equation:
(V)(1 atm) = (0.2292 mol)(0.0821 L x atm/(mol x K))(298 K)
Simplifying the equation:
V = (0.2292 mol)(0.0821 L x atm/(mol x K))(298 K) / (1 atm)
V = 5.6863 L
Therefore, the volume of hydrogen gas produced is 5.6863 liters at 25°C and 1 atm.
To find the volume of hydrogen gas produced, we need to determine the moles of zinc and then use the stoichiometry of the reaction to find the moles of hydrogen gas produced. Finally, we can use the ideal gas law to find the volume of hydrogen gas.
Step 1: Convert grams of zinc to moles
The molar mass of zinc (Zn) is 65.38 g/mol.
moles of Zn = mass of Zn / molar mass of Zn
moles of Zn = 15.00 g / 65.38 g/mol
Step 2: Use the balanced equation to determine the moles of hydrogen gas produced
From the balanced chemical equation, we can see that 1 mole of zinc (Zn) reacts with 2 moles of hydrochloric acid (HCl) to produce 1 mole of hydrogen gas (H2).
moles of H2 = moles of Zn * (1 mole of H2 / 1 mole of Zn)
Step 3: Use the ideal gas law to find the volume of hydrogen gas
The ideal gas law is given by the equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Rearranging the equation, we get:
V = (nRT) / P
Given:
P = 1.00 atm
T = 25°C = 25 + 273.15 = 298.15 K (conversion from Celsius to Kelvin)
Now, substitute the values into the equation to find the volume of hydrogen gas:
V = (moles of H2 * R * T) / P
Remember to use the appropriate value for the ideal gas constant (R). The commonly used value is 0.0821 L·atm/(mol·K).
By following these steps, you should be able to calculate the volume of hydrogen gas produced when 15.00 g of zinc reacts with 100.0 mL of 4.00 M hydrochloric acid at 25°C and 1.00 atm.
15g Zn = 0.229 moles
100mL of 4M HCl = 0.4 moles
Zn + 2HCl -> ZnCl2 + H2
The 0.4 moles of HCl are used up first, producing 0.2 moles of H2
Now recall that 1 mole of H2 at STP occupies 22.4L and finish up using PV=kT