A common laboratory preparation of hydrogen on a small scale uses the reaction of zinc with hydrochloric acid. Zinc chloride is the other product.
(a) If 13.0 L of H2 at 765 torr and 20.0 °C is wanted, how many grams of zinc are needed, in theory?
(b) If the acid is available as 8.59 M HCl, what is the minimum volume of this solution (in milliliters) required to produce the amount of H2 described in part (a)?
Zn + 2HCl ==> H2 + ZnCl2
Use PV = nRT and solve for n = number of mols H2 at the conditions listed. Convert mols H2 to mols Zn, then
g Zn = mols Zn x atomic mass Zn.
b)
Convert mols H2 to mols HCl, then M HCl = mols HCl/L HCl. Solve for L and convert to mL.
(a) Well, let's get theoretical for a moment! To figure out how many grams of zinc are needed, we need to use the ideal gas law to calculate the number of moles of hydrogen.
PV = nRT
Where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles, R is the ideal gas constant (0.0821 L.atm/mol.K), and T is the temperature in Kelvin.
First, let's convert the temperature to Kelvin:
20.0 °C + 273 = 293 K
Now, let's plug in the values we have:
(765 torr)(13.0 L) = n(0.0821 L.atm/mol.K)(293 K)
Solving for n gives us:
n = (765 torr)(13.0 L) / (0.0821 L.atm/mol.K)(293 K)
Now, we know that according to the balanced chemical equation, 1 mole of zinc reacts with 1 mole of hydrogen. So the number of moles of zinc needed is the same as the number of moles of hydrogen.
Once we have the number of moles, we can calculate the mass of zinc using its molar mass.
(b) Oh, the chemistry is getting spicy now! To figure out the minimum volume of the 8.59 M HCl solution required to produce the desired amount of H2, we need to use the molarity formula.
Molarity (M) = moles of solute / volume of solution in liters
First, let's calculate the moles of hydrogen using the ideal gas law as we did in part (a). Once we have that, we'll then have the moles of zinc since we know it reacts on a 1:1 ratio with hydrogen.
Now, to figure out the volume of the 8.59 M HCl solution needed, we rearrange the molarity formula:
Volume of solution (in liters) = moles of solute / Molarity
So, we divide the moles of zinc by the molarity of the HCl solution to find the minimum volume needed. Don't forget to convert it into milliliters to get the final answer!
To answer these questions, we need to use the stoichiometry of the reaction between zinc and hydrochloric acid to calculate the necessary quantities.
The balanced chemical equation for the reaction is:
Zn + 2HCl -> ZnCl2 + H2
(a) To determine the amount of zinc needed to produce a given quantity of hydrogen, we need to use the ideal gas law 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. Rearranging the equation, we have:
n = PV / RT
Given:
P = 765 torr
V = 13.0 L
T = 20.0 °C = 293 K (converted to Kelvin by adding 273)
Rearranging the equation, we have:
n(H2) = (765 torr * 13.0 L) / (0.0821 L.atm/mol.K * 293 K)
n(H2) ≈ 41.93 moles of H2
From the balanced chemical equation, we know that 1 mole of Zn reacts with 1 mole of H2. So, the amount of zinc needed in moles would be equal to the amount of hydrogen:
n(Zn) ≈ 41.93 moles of Zn
The molar mass of zinc (Zn) is approximately 65.38 g/mol. Therefore, the mass of zinc needed in grams is:
Mass(Zn) = n(Zn) * molar mass(Zn)
Mass(Zn) ≈ 41.93 moles * 65.38 g/mol ≈ 2744.16 g
Therefore, approximately 2744.16 grams of zinc are needed in theory to produce 13.0 L of hydrogen at 765 torr and 20.0 °C.
(b) To calculate the minimum volume of 8.59 M HCl solution needed to produce the amount of hydrogen described in part (a), we can use the molarity equation:
M1V1 = M2V2
where M1 and V1 are the molarity and volume of the initial solution, and M2 and V2 are the molarity and volume of the final solution.
Given:
M1 = 8.59 M
V1 = volume to be calculated
M2 = 2 (from the balanced chemical equation)
V2 = 13.0 L
Rearranging the equation, we have:
V1 = (M2 * V2) / M1
V1 = (2 * 13.0 L) / (8.59 M)
V1 ≈ 2.33 L (converted to milliliters by multiplying by 1000)
Therefore, approximately 2330 milliliters (or 2.33 liters) of 8.59 M HCl solution are needed to produce the amount of hydrogen described in part (a).
To find the number of grams of zinc needed in theory, we need to use stoichiometry, which involves balancing the equation and using the molar ratios.
The balanced equation for the reaction is:
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
(a) First, let's calculate the number of moles of H2 gas using the ideal gas law equation:
PV = nRT
Given:
P = 765 torr
V = 13.0 L
T = 20.0 °C = 293.15 K (convert to Kelvin)
Converting the pressure to atm: 765 torr / 760 torr/atm = 1.00658 atm
Plugging in the values into the ideal gas law equation:
(1.00658 atm) * (13.0 L) = n * (0.0821 L*atm/mol*K) * (293.15 K)
Solving for n, the number of moles of H2 gas:
n = (1.00658 atm * 13.0 L) / (0.0821 L*atm/mol*K * 293.15 K) ≈ 0.563 moles
According to the balanced equation, for every 1 mole of H2 gas produced, 1 mole of zinc is consumed. Therefore, the number of moles of zinc required is also 0.563 moles.
(b) Now, let's find the minimum volume of 8.59 M HCl solution required to produce 0.563 moles of H2 gas.
First, convert the given concentration from moles/L to moles/mL:
8.59 M = 8.59 moles/L = 8.59 moles/1000 mL
Using the equation:
moles = concentration * volume
Plugging in the values and solving for volume in milliliters:
0.563 moles = (8.59 moles/1000 mL) * volume
volume = (0.563 moles) / (8.59 moles/1000 mL) ≈ 65.5 mL
Therefore, the minimum volume of 8.59 M HCl solution required is approximately 65.5 mL.