What is the percent yield of #O_2# if 10.2 g of #O_2# is produced from the decomposition of 17.0 g of #H_2O#?

Question

Owen Ambrose · Accepted Answer

#%Yield=67.5%#

You can compute the percent yield by:

#%Yield=("Actual Yield")/("Theoretical Yield")xx100%#

The actual yield of oxygen is given and it is #10.2g#.

The theoretical yield must be determined.

The water's breakdown reaction can be expressed as follows:

#2H_2O(l)->2H_2(g)+O_2(g)#

We will use dimensional analysis to determine the theoretical yield of oxygen:

#?g O_2=underbrace(17.0gH_2Oxx(1molH_2O)/(18.0gH_2O))_(color(blue)("g to mol"))xxunderbrace((1molO_2)/(2molH_2O))_color(green)("molar ratio")xxunderbrace((32.0gO_2)/(1molO_2))_(color(red)("mol to g"))=15.1gO_2#

Thus, the theoretical yield is equal to #15.1g#.

The percent yield is then: #%Yield=(10.2)/(15.1)xx100%=67.5%#

Luna Chen · Answer

undefined To calculate the percent yield of O2, we first need to determine the theoretical yield of O2 based on the given amount of H2O and then compare it to the actual yield.

1. Calculate the molar mass of H2O:
   Molar mass of H2O = 2(1.008 g/mol) + 16.00 g/mol = 18.02 g/mol

2. Convert the mass of H2O to moles:
   Moles of H2O = 17.0 g / 18.02 g/mol = 0.943 mol

3. According to the balanced chemical equation for the decomposition of water:
   2H2O → 2H2 + O2

We see that for every 2 moles of water decomposed, 1 mole of O2 is produced. Therefore, the theoretical yield of O2 is half the number of moles of H2O.

4. Calculate the theoretical yield of O2:
   Theoretical yield of O2 = 0.943 mol H2O × (1 mol O2 / 2 mol H2O) = 0.472 mol

5. Convert the theoretical yield of O2 from moles to grams:
   Theoretical yield of O2 = 0.472 mol × 32.00 g/mol = 15.1 g

6. Now, calculate the percent yield using the actual yield:
   Percent yield = (actual yield / theoretical yield) × 100%
                 = (10.2 g / 15.1 g) × 100%
                 ≈ 67.5%

Therefore, the percent yield of O2 from the decomposition of 17.0 g of H2O is approximately 67.5%.