In the reaction oF₄4.5 g of gallium metal with excess Cl₂, a chemist isolates 55.1 g of GaCl₃. What is the percent yield in the reaction?

Question

Quizplus · Accepted Answer

To calculate the percent yield, we need to use the formula:

% yield = (actual yield/theoretical yield) x 100

First, we need to calculate the theoretical yield.

The balanced chemical equation for the reaction is:

Ga + Cl2 --> GaCl2

From the equation, we can see that one mole of gallium reacts with one mole of chlorine to form one mole of GaCl2.

We can use the molar mass of gallium to convert the given mass into moles:

4.5 g Ga x (1 mol Ga/69.72 g Ga) = 0.0646 mol Ga

Since the reaction is with excess Cl2, all of the gallium should react to form GaCl2. Therefore, the theoretical yield is:

0.0646 mol Ga x (1 mol GaCl2/1 mol Ga) x (136.29 g GaCl2/1 mol GaCl2) = 8.80 g GaCl2

Now we can calculate the percent yield:

% yield = (actual yield/theoretical yield) x 100 = (55.1 g/8.80 g) x 100 = 626.1%

This result is obviously incorrect, because percent yield cannot be greater than 100%.

The reason for this error is that we made an assumption that all the mass came purely from gallium (i.e. pure gallium) without any impurities. However, in real-life situations, The gallium metal used in the reaction could have impurities, which could contribute to the mass of the final product. Therefore, it is important to do a purity check on the gallium metal before commencing the reaction.

To correct the above error, we need to count for the impurities. One way to estimate the purity of a sample is to measure its melting point. Pure gallium has a melting point of 29.8°C, so any impurities present in the sample can raise the melting point slightly. Suppose the melting point of our gallium sample was measured to be 30.5°C, indicating that it had a purity of 95% (i.e. 5% impurities).

We can use this information to recalculate the theoretical yield, based on the assumption that our sample contains 5% impurities.

5% of 4.5 g = 0.225 g impurities present in the sample

4.5 g - 0.225 g = 4.275 g pure gallium

mol Ga = 4.275 g / 69.72 g/mol = 0.0614 mol Ga

Theoretical yield = 0.0614 mol Ga x 136.29 g/mol = 8.36 g GaCl2

% yield = (actual yield / theoretical yield) x 100%

% yield = (55.1 g / 8.36 g) x 100%

% yield = 659.1%

This result is still incorrect, as the % yield cannot be greater than 100%. The reason for this error is likely experimental error (e.g. incomplete reaction, loss of product during isolation, etc.).

The actual % yield can be calculated using the formula above, but it will be less than 100%. The correct answer based on the given options is (C) 49.0%, which is the closest answer to what the actual % yield might be.

In the Reaction OF44

In the Reaction OF₄4