According to the Law of Conservation of Mass, the mass of the reactants must equal the mass of the products in a chemical reaction.
Given that 98 g of carbon dioxide (CO2) is produced and 24 g of carbon (C) is used in the reaction, we can calculate the mass of dioxygen (O2) in the reactants as follows:
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First, we can find out the mass of oxygen in the carbon dioxide produced. The molar mass of CO2 is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Molar mass of CO2 = 12 g/mol + (2 × 16 g/mol) = 12 g/mol + 32 g/mol = 44 g/mol
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Next, calculate the mass of oxygen in 98 g of CO2. Since the molar mass of CO2 is 44 g, we can find the fraction of the mass that is due to oxygen: \[ \text{Mass of oxygen in CO2} = \text{Total mass of CO2} - \text{mass of carbon} = 98 , \text{g} - 24 , \text{g} = 74 , \text{g} \]
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Since the mass of the reactants equals the mass of the products, we can determine the mass of dioxygen (O2):
- The mass of oxygen from O2 would be equal to the mass of oxygen in CO2, which is part of what got transformed during the reaction to form CO2.
To find the mass of O2 required to provide this oxygen, we can consider that there are 2 oxygen atoms in CO2. Thus, if 74 g of O comes from O2, \[ \text{Mass of O2} = \text{Mass of O} / 2 = 74 , \text{g} / 2 = 37 , \text{g} \quad \text{(This tells us how much O2 was needed)} \]
- The total mass of the reactants, including the 24 g of carbon and the O2, must add up to the total mass (98 g).
To find the mass of O2 (since only half of O2 constitutes the mass of O), \[ \text{Mass of O2} = 74 , \text{g} , \text{(mass of O found before)} \]
Thus: The total mass of reactants is 24 g (C) + \(x \) (mass of dioxygen (O2)), therefore, \[ 24 \text{ g} + x = 98 \text{ g} \] \[ x = 98 \text{ g} - 24 \text{ g} = 74 \text{ g} \]
Thus, the mass of dioxygen (O2) in the reactants is 74 g.
Final answer: 74 g.