A student reacts 0.1212 g of an Mg/NaCl mixture with hydrochloric acid. The volume of hydrogen saturated with water vapor collected at 20.0C was measured to be 42.7 ml. The column of water that remained in the buret was 10.3 cm high. If vapor pressure of water = 17.5 mmHg at this temperature and the barometric pressure was 763 mmHg, what is the % Mg in the sample?
Mass %=(0.0418/0.1212)x100=34.499%
15%
To find the percentage of Mg in the sample, we need to determine the number of moles of Mg present in the reaction mixture. Here's how you can calculate it:
Step 1: Calculate the Partial Pressure of Hydrogen Gas
The volume of hydrogen collected is given as 42.7 ml. However, we need to correct this volume to account for the presence of water vapor. To do this, we subtract the vapor pressure of water (17.5 mmHg) from the total pressure:
Partial pressure of hydrogen = Total pressure - Vapor pressure of water
Partial pressure of hydrogen = 763 mmHg - 17.5 mmHg
Partial pressure of hydrogen = 745.5 mmHg
Step 2: Convert Volume to Moles
We can use the ideal gas law to convert the volume of hydrogen gas to moles. The ideal gas law equation is:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the pressure to atm and the temperature to Kelvin:
Pressure (in atm) = 745.5 mmHg / 760 mmHg/atm ≈ 0.980
Temperature (in Kelvin) = 20.0C + 273.15 = 293.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (0.980 atm) * (0.0427 L) / (0.0821 L·atm/(mol·K) * 293.15 K
Calculating this value, we find:
n ≈ 0.00183 mol
Step 3: Calculate Moles of Mg
Based on the balanced chemical equation for the reaction between Mg and HCl, we know that 1 mole of Mg reacts with 2 moles of HCl to produce 1 mole of hydrogen gas. Therefore, the number of moles of magnesium present is half of the number of moles of hydrogen:
Number of moles of Mg ≈ 0.00183 mol / 2 ≈ 0.000915 mol
Step 4: Calculate Percentage of Mg
Finally, we can calculate the percentage of Mg in the sample:
% Mg = (moles of Mg / total mass of sample) * 100
To find the total mass of the sample, we need to assume a mass for the sample. However, the mass is not provided in the given information. Therefore, without knowing the mass of the sample, we cannot calculate the percentage of Mg.
In summary, the calculation of the percentage of Mg in the sample requires knowledge of the total mass of the sample, which is not given in the problem statement.