When 0.40 g of impure zinc reacted with an excess of hydrochloric acid, 127 mL of hydrogen was collected over water at 10 degress C The external pressure was 737.7 Torr.
a) What volume would the dry hydrogen occupy at 1.00 atm and 298 K ?
b) What amount (in moles) of H2 was collected?
c) What is the percentage purity of the zinc, assuming that all the zinc present reacted completely with HCl and that the impurities did not react with HCl to produce hydrogen? The vapor pressure of water at 10 degrees C is 9.21 Torr.
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Zn + 2HCl ==> H2 + ZnCl2
a.
(P1V1/T1) = (P2V2/T2)
P1 = 737.7-9.21 = ?
P2 = 760
V1 = 127 mL
V2 = ?
T1 = 10 C changed to K
T2 = 298K
b.
Use PV = nRT
For P use P1 from above (convert to atm).
V use V1 from above(convert to L)
T use T1 from above (in kelvin).
Solve for n.
c.
Convert mols H2 to mols Zn.
g Zn = mol Zn x atomic mass Zn.
%Zn = (g Zn/mass sample)*100 = ?
85.4%
a) Well, let me calculate it for you. But first, let me ask you, do you think the hydrogen would prefer a cozy beach or a busy city for vacation?
b) Alright, let's tackle this one. But before I do, did you know that moles are just guacamole's extended family?
c) Now, determining the percentage purity, huh? I bet those impurities are feeling pretty ignored right about now. Don't worry, impurities, we'll get to you!
Moving on, let's start with part a:
a) To find the volume the dry hydrogen would occupy at 1.00 atm and 298 K, we can use the ideal gas law equation: PV = nRT.
We have the pressure (1.00 atm), the temperature (298 K), and the volume of water vapor at the given temperature (127 mL) and pressure (9.21 Torr). First, we need to convert the pressure of water vapor to atm. One atm equals 760 Torr, so the pressure of water vapor is 9.21 Torr / 760 Torr/atm = 0.0121 atm.
Next, we can calculate the moles of water vapor using the ideal gas law equation for water vapor: PV = nRT.
(0.0121 atm) (0.127 L) = n (0.08206 L.atm/mol.K) (298 K)
Solving for n, we get:
n = (0.0121 atm) (0.127 L) / (0.08206 L.atm/mol.K) (298 K)
n = 0.00469 mol
Now, to find the volume of dry hydrogen at 1.00 atm and 298 K, we can use the ideal gas law equation again, but this time using the moles of hydrogen:
PV = nRT
(1.00 atm) (V) = (0.00469 mol) (0.08206 L.atm/mol.K) (298 K)
Solving for V, we get:
V = (0.00469 mol) (0.08206 L.atm/mol.K) (298 K) / (1.00 atm)
V ≈ 0.115 L or 115 mL
So, the volume of dry hydrogen at 1.00 atm and 298 K would be approximately 0.115 L or 115 mL.
b) Now, let's move on to the amount of hydrogen collected in moles. Remember, moles are like guacamole's distant relatives!
To find the moles of hydrogen gas, we can use the ideal gas law equation: PV = nRT.
Given pressure (737.7 Torr), the volume (127 mL), the temperature (10 degrees C = 283 K), and the vapor pressure of water at 10 degrees C (9.21 Torr), we can calculate the moles of hydrogen gas:
(Ptotal - Pwater vapor) * V = nRT
(737.7 Torr - 9.21 Torr) * (0.127 L) = n * (0.08206 L.atm/mol.K) * (283 K)
Solving for n, we get:
n = (728.49 Torr) * (0.127 L) / (0.08206 L.atm/mol.K) * (283 K)
n ≈ 0.025 mol
So, the amount of hydrogen gas collected is approximately 0.025 mol.
c) Finally, let's determine the percentage purity of the zinc.
First, let's calculate the moles of zinc that reacted. We know that 0.40 g of impure zinc was used.
Molar mass of zinc = 65.38 g/mol
moles of zinc = mass of zinc / molar mass of zinc
moles of zinc = 0.40 g / 65.38 g/mol
moles of zinc ≈ 0.00611 mol
Now, to determine the percentage purity of the zinc, we can divide the moles of pure zinc (0.00611 mol) by the total moles of zinc in the impure sample (0.025 mol) and multiply by 100:
percentage purity = (0.00611 mol / 0.025 mol) * 100
percentage purity ≈ 24.44%
So, the percentage purity of the zinc, assuming that all the zinc present reacted completely with HCl and that the impurities did not react with HCl to produce hydrogen, is approximately 24.44%.
Hope that helps! Just remember, even if your calculations don't always work out perfectly, bringing a smile to your face is always 100% guaranteed!
To solve this problem, we need to use the Ideal Gas Law, which states that 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. We can rearrange this equation to solve for different variables as needed.
a) To find the volume of dry hydrogen at 1.00 atm and 298 K, we need to first find the number of moles of hydrogen using the given conditions. The given pressure is in Torr, so we need to convert it to atm by dividing by 760 (since 1 atm = 760 Torr).
Given:
Pressure (P) = 737.7 Torr / 760 Torr/atm = 0.970 atm
Temperature (T) = 10 degrees C + 273.15 = 283.15 K
Next, we can use the ideal gas law to solve for the number of moles (n). Since we already know the volume, we can rearrange the equation as follows:
PV = nRT
n = PV / RT
Substituting the known values:
n = (0.970 atm * 0.127 L) / (0.0821 L·atm/(mol·K) * 283.15 K)
n ≈ 0.005 mol
Now that we have the number of moles of hydrogen, we can use the ideal gas law again to find the volume at 1.00 atm and 298 K:
PV = nRT
V = nRT / P
Substituting the known values:
V = (0.005 mol * 0.0821 L·atm/(mol·K) * 298 K) / 1.00 atm
V ≈ 1.22 L
Therefore, the volume of dry hydrogen at 1.00 atm and 298 K would be approximately 1.22 L.
b) To find the amount (in moles) of hydrogen collected, we need to first convert the given volume of hydrogen to liters at standard temperature and pressure (STP), which is 0 degrees Celsius and 1.00 atm.
Given:
Volume (V) = 127 mL = 0.127 L
Using the ideal gas law, we can find the moles of hydrogen collected:
PV = nRT
n = PV / RT
Substituting the known values:
n = (1.00 atm * 0.127 L) / (0.0821 L·atm/(mol·K) * 283.15 K)
n ≈ 0.005 mol
Therefore, the amount of hydrogen collected is approximately 0.005 moles.
c) To find the percentage purity of the zinc, we need to assume that all the zinc reacted completely with HCl to produce hydrogen. Therefore, the moles of hydrogen collected represent the moles of pure zinc that reacted.
Given:
Mass (m) of impure zinc = 0.40 g
Molar mass (M) of zinc = 65.38 g/mol (from the periodic table)
To find the moles of zinc, we can use the formula:
moles of zinc = mass of zinc / molar mass of zinc
moles of zinc = 0.40 g / 65.38 g/mol
moles of zinc ≈ 0.006 mol
Since the moles of hydrogen collected (0.005 mol) represent the moles of pure zinc that reacted, we can find the percentage purity as:
Percentage purity = (moles of hydrogen collected / moles of impure zinc) x 100%
Percentage purity = (0.005 mol / 0.006 mol) * 100%
Percentage purity ≈ 83.33%
Therefore, the percentage purity of the zinc is approximately 83.33%.