A 0.411 g sample of powdered copper mixed with an inert, soluble additive was fully consumed by 23.4mL of 0.602M nitric acid, producing copper (II) nitrate, water, and nitric oxide. What is the percent copper by mass in the sample?
3Cu + 8HNO3 = 3Cu(NO3)2 +2NO =4H2O
Dear Veronica,
number of moles of HNO3 used=
0.602x(23.4/1000)
= 0.014
number of mol of Cu used=
0.014/8x3
=5.28255x10^-3
mass of the Cu involved in the reaction
= 5.28255x10^-3 x 63.5
= 0.33544g
%by mass of Cu =
0.33544/0.411 x 100%
= 81.6%
To calculate the percent copper by mass in the sample, we need to determine the mass of copper in the sample and divide it by the mass of the entire sample, then multiply by 100.
Here are the steps to solve the problem:
1. Calculate the amount of copper reacted:
a. Convert the volume of nitric acid used to moles by multiplying it by the molarity:
23.4 mL * 0.602 mol/L = 14.083 mol
b. According to the balanced equation, the stoichiometric ratio between copper and nitric acid is 3:8. So, we can determine the moles of copper:
Moles of Copper = 3/8 * Moles of Nitric Acid
= 3/8 * 14.083 mol
= 5.264 mol
2. Calculate the mass of copper reacted:
a. Multiply the moles of copper by the molar mass of copper:
Mass of Copper = Moles of Copper * Molar Mass of Copper
= 5.264 mol * 63.546 g/mol
= 334.03 g
3. Calculate the percent copper by mass in the sample:
a. Divide the mass of copper by the initial sample mass and multiply by 100:
Percent Copper = (Mass of Copper / Initial Sample Mass) * 100
= (334.03 g / 0.411 g) * 100
= 81228%
Therefore, the percent copper by mass in the sample is approximately 81228%.
To find the percent copper by mass in the sample, you need to calculate the amount of copper in the sample and compare it to the total mass.
Let's set up the stoichiometry of the reaction first:
3Cu + 8HNO3 → 3Cu(NO3)2 + 2NO + 4H2O
From the balanced equation, we can see that 3 moles of copper react with 8 moles of nitric acid to produce 3 moles of copper (II) nitrate, 2 moles of nitric oxide, and 4 moles of water.
Here are the steps to calculate the percent copper by mass:
1. Calculate the number of moles of nitric acid used:
Moles of nitric acid = volume of nitric acid (in L) × molarity of nitric acid
Given: volume of nitric acid = 23.4 mL = 0.0234 L, molarity of nitric acid = 0.602 M
Moles of nitric acid = 0.0234 L × 0.602 M = 0.0140768 mol
2. Use the stoichiometry of the balanced equation to determine the number of moles of copper used:
From the balanced equation, 3 moles of copper reacts with 8 moles of nitric acid. Therefore, the number of moles of copper used is:
Moles of copper = (3/8) × moles of nitric acid
Moles of copper = (3/8) × 0.0140768 mol = 0.0052773 mol
3. Calculate the mass of copper used:
Mass of copper used = moles of copper × molar mass of copper
The molar mass of copper (Cu) is 63.546 g/mol.
Mass of copper used = 0.0052773 mol × 63.546 g/mol = 0.3350 g
4. Calculate the percent copper by mass:
Percent copper by mass = (mass of copper used / mass of sample) × 100
Given: mass of sample = 0.411 g
Percent copper by mass = (0.3350 g / 0.411 g) × 100 = 81.6%
Therefore, the percent copper by mass in the sample is approximately 81.6%.