Pergunta
Determine the empirical formula for a compound with 59.9% C. 8.06% H. 32.0% O square
Solução
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JoãoProfissional · Tutor por 6 anos
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Let's perform the calculations:<br /><br />For Carbon (C): <br />\[<br />\frac{{59.9 \text{{ g}}}}{{12.01 \text{{ g/mol}}}} = 4.99 \text{{ moles}}<br />\]<br /><br />For Hydrogen (H): <br />\[<br />\frac{{8.06 \text{{ g}}}}{{1.008 \text{{ g/mol}}}} = 8.02 \text{{ moles}}<br />\]<br /><br />For Oxygen (O): <br />\[<br />\frac{{32.0 \text{{ g}}}}{{16.00 \text{{ g/mol}}}} = 2.00 \text{{ moles}}<br />\]<br /><br />The smallest number of moles is 2.00 (for O). So, we divide each by 2.00 to get the simplest whole number ratio:<br /><br />For C: <br />\[<br />\frac{{4.99}}{{2.00}} = 2.495 \approx 2.5<br />\]<br /><br />For H: <br />\[<br />\frac{{8.02}}{{2.00}} = 4.01 \approx 4<br />\]<br /><br />For O: <br />\[<br />\frac{{2.00}}{{2.00}} = 1<br />\]<br /><br />So, the empirical formula for the compound is \(C_{2.5}H_{4}O\). However, empirical formulas should only contain whole numbers. To correct this, we can multiply all subscripts by 2 to get rid of the decimal, resulting in \(C_{5}H_{8}O_{2}\).
Explicação
## Step 1: <br />First, we need to convert the percentages of each element in the compound to grams. This is because the empirical formula is based on the simplest whole number ratio of atoms in a compound, which can be determined by comparing the number of moles of each element.<br /><br />## Step 2: <br />Next, we convert the grams of each element to moles using their respective molar masses. The molar mass of carbon (C) is approximately 12.01 g/mol, hydrogen (H) is approximately 1.008 g/mol, and oxygen (O) is approximately 16.00 g/mol.<br /><br />## Step 3: <br />After finding the number of moles of each element, we divide each by the smallest number of moles calculated to get the simplest whole number ratio of atoms.<br /><br />### The formula for this step is: <br />\[<br />\text{{Ratio of atoms}} = \frac{{\text{{Number of moles of each element}}}}{{\text{{Smallest number of moles}}}}<br />\]<br /><br />## Step 4: <br />Finally, we write the empirical formula using the whole number ratios obtained in the previous step.
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