Calculate the percent purity of a sample of zinc metal if 325 mL of hydrogen gas is collected by water displacement at a temperature of 22.0 C and an atmospheric pressure of 745.0 mm Hg when 1.12 g of the sample is reacted with excess HCl: Zn + 2 HCl = H2 + ZnCl2. The vapor pressure of water at 22.0 C is 19.8 mm Hg. Assume that any impurities in the zinc metal do not react with HCl.
Use PV = nRT and solve for n = number of moles at the conditions listed.
For p you must use ptotal = pH2 + pH2O
ptotal = 745 mm
pH2O = 19.8 mm from the problem. Solve for pH2 (which is dry H2), then remember to convert to atm. 760 mm = 1 atm.
When you have n, that's mols H2.
From the equation 1 mol H2 = 1 mol Zn
Then g Zn = mols Zn x atomic mass Zn.
%Zn = (g Zn/mass sample)*100 = ?
To calculate the percent purity of the sample of zinc metal, we need to determine the amount of hydrogen gas produced and compare it to the theoretical amount that should have been produced if the sample was 100% pure.
1. First, let's calculate the moles of hydrogen gas produced using the ideal gas law:
PV = nRT
Where:
P = total pressure = atmospheric pressure - vapor pressure of water
V = volume of hydrogen gas collected
n = moles of hydrogen gas
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature in Kelvin
Convert the temperature from Celsius to Kelvin:
T = 22.0°C + 273.15 = 295.15 K
Calculate the total pressure:
P = 745.0 mm Hg - 19.8 mm Hg = 725.2 mm Hg
Convert the total pressure to atm:
P = 725.2 mm Hg / 760 mm Hg/atm = 0.954 atm
2. Convert the volume of hydrogen gas collected to liters:
325 mL = 325 mL * (1 L / 1000 mL) = 0.325 L
3. Plug in the values into the ideal gas law equation to calculate the moles of hydrogen gas:
0.954 atm * 0.325 L = n * 0.0821 L·atm/(mol·K) * 295.15 K
Solve for n:
n = (0.954 atm * 0.325 L) / (0.0821 L·atm/(mol·K) * 295.15 K)
n ≈ 0.0137 mol
4. The balanced equation tells us that 1 mole of zinc reacts to produce 1 mole of hydrogen gas:
Zn + 2 HCl → H2 + ZnCl2
5. Since 1.12 g of the sample produced 0.0137 mol of hydrogen gas, we can calculate the molar mass of zinc to determine the percent purity.
Molar mass of zinc (Zn) = 65.38 g/mol
6. Calculate the theoretical amount of zinc in the sample:
Theoretical amount of zinc = molar mass of zinc * moles of hydrogen gas
Theoretical amount of zinc = 65.38 g/mol * 0.0137 mol ≈ 0.896 g
7. Finally, calculate the percent purity:
Percent purity = (actual amount of zinc / theoretical amount of zinc) * 100
Percent purity = (1.12 g / 0.896 g) * 100
Percent purity ≈ 125.0%
Therefore, the percent purity of the sample of zinc metal is approximately 125.0%.
To calculate the percent purity of the zinc metal sample, we can follow these steps:
Step 1: Calculate the pressure of hydrogen gas collected.
Given:
- Atmospheric pressure: 745.0 mm Hg
- Vapor pressure of water: 19.8 mm Hg
The pressure of hydrogen gas can be calculated by subtracting the vapor pressure of water from the total atmospheric pressure:
Pressure of hydrogen gas = Atmospheric pressure - Vapor pressure of water
Pressure of hydrogen gas = 745.0 mm Hg - 19.8 mm Hg
Pressure of hydrogen gas = 725.2 mm Hg
Step 2: Convert the volume of hydrogen gas collected to standard conditions.
Given:
- Volume of hydrogen gas: 325 mL
To compare the volume of gas at different conditions, we need to convert it to standard conditions, which are usually at 0 degrees Celsius and 1 atmosphere of pressure (760 mm Hg). We can use the ideal gas law equation to solve for the volume at standard conditions:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = pressure at initial conditions (725.2 mm Hg)
V1 = volume at initial conditions (325 mL)
T1 = temperature at initial conditions (22.0 C + 273.15 K)
P2 = pressure at standard conditions (760 mm Hg)
V2 = unknown volume at standard conditions
T2 = temperature at standard conditions (0.0 C + 273.15 K)
Now we solve for V2:
(725.2 mm Hg * 325 mL) / (22.0 C + 273.15 K) = (760 mm Hg * V2) / (0.0 C + 273.15 K)
V2 = (725.2 mm Hg * 325 mL * (0.0 C + 273.15 K)) / (760 mm Hg * (22.0 C + 273.15 K))
V2 = 301.1 mL
Step 3: Calculate the number of moles of hydrogen gas.
Using the ideal gas law equation, we can calculate the number of moles of gas:
PV = nRT
Where:
P = pressure (760 mm Hg)
V = volume (301.1 mL)
n = unknown number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (0.0 C + 273.15 K)
Now we solve for n:
(760 mm Hg * 301.1 mL) = n * (0.0821 L·atm/(mol·K)) * (0.0 C + 273.15 K)
n = (760 mm Hg * 301.1 mL) / (0.0821 L·atm/(mol·K) * 273.15 K)
n = 0.0128 mol
Step 4: Calculate the number of moles of zinc.
Looking at the balanced chemical equation:
Zn + 2 HCl = H2 + ZnCl2
We can see that the ratio between Zn (zinc) and H2 (hydrogen gas) is 1:1. This means that the number of moles of zinc is equal to the number of moles of hydrogen gas.
So, the number of moles of zinc = 0.0128 mol
Step 5: Calculate the molar mass of zinc.
The molar mass of zinc (Zn) is approximately 65.38 g/mol.
Step 6: Calculate the mass of the zinc sample.
From the given information, the mass of the zinc sample is given as 1.12 g.
Step 7: Calculate the percent purity.
To calculate the percent purity, we use the formula:
Percent purity = (mass of pure substance / mass of sample) x 100
Percent purity = (mass of zinc / mass of sample) x 100
Percent purity = (0.0128 mol * 65.38 g/mol / 1.12 g) x 100
Percent purity = 749%
Therefore, the percent purity of the zinc metal sample is 749%.