If a sample of C4H8O3 is found to contain 3.89 g of C atoms, how many grams of O atoms are present in the sample?

Question

BlackTom AI · Accepted Answer

To tackle this problem, I’ll first restate what we know and then examine each answer choice.

The compound is C4H8O3. In one mole of this compound:
- Carbon mass = 4 × 12 = 48 g
- Oxygen mass = 3 × 16 = 48 g
- Total molar mass = 48 + 8 × 1 + 48 = 104 g (using approximate integer masses)
Thus, the mass fraction of carbon in the compound equals the mass fraction of oxygen, each contributing 48 g per 104 g of compound. Consequently, in any sample, the mass of oxygen atoms present is essentially equal to the mass of carbon atoms present, assuming the sample contains only these elements.

Option 1: 0.778 g
- This value is far smaller than what we’d expect given that mass fractions for C and O are equal and the sample’s carbon mass is 3.89 g. If C and O were equal, O should be around 3.89 g, not 0.778 g. This option seems to come from a miscalculation of the ratio or a misapplication of molar masses.

Option 2: 0.973 g
- This is also inconsistent with the equal C and O mass fractions. If the carbon mass is 3.89 g, and C and O contribute equally per mole, the oxygen mass should be near 3.89 g, not approximately 1 g. This option reflects another incorrect proportional calculation.

Option 3: 5.18 g
- This value is larger than the total mass of carbon in the sample would imply if there were a fixed total sample mass with C contributing 3.89 g. It overestimates the oxygen content by misapplying the mass-fraction relationship or adding masses beyond what the carbon mass dictates.

Option 4: 2.92 g
- This is closer in magnitude to the carbon mass, but it still ignores the key fact that C and O contribute equal masses per mole of C4H8O3. Unless there’s some stated limitation (e.g., partial decomposition or impurity), this would not be the correct equal-mass outcome given the problem’s setup.

Option 5: 3.89 g
- This option matches the principle that C and O contribute equal masses per mole in C4H8O3, since both carbon and oxygen contribute 48 g per 104 g of compound. Therefore, for a sample where the mass of carbon atoms is 3.89 g, the mass of oxygen atoms in the same sample would also be 3.89 g if the sample consists of only C, H, and O in the specified ratio.

Across these choices, the correct relational fact is that C and O have equal mass contributions in one mole of C4H8O3, so the oxygen mass mirrors the given carbon mass. The remaining options reflect common mistakes like applying incorrect mass fractions, mixing up total masses, or misapplying the ratio of elements in the formula.

If a sample of C4H8O3 is found to contain 3.89 g of C atoms, how many grams of O atoms are present in the sample?

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