This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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You're on a roll — Step 1: Write the balanced chemical equation for the combustion of methane. The reaction of methane (CH_4) with oxygen (O_2) produces carbon dioxide (CO_2) and water (H_2O). Since the water formed is neglected, it is considered to be in the liquid state. CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(l) Step 2: Determine the volume of oxygen that reacted. Initial volume of oxygen = 48 cm^3 Unused oxygen = 24.0 cm^3 Volume of O_2 reacted = Initial volume of O_2 - Unused O_2 Volume of O_2 reacted = 48 cm^3 - 24.0 cm^3 = 24.0 cm^3 Step 3: Determine the volume of methane that reacted and the volume of carbon dioxide produced using the stoichiometric ratio. From the balanced equation, the ratio of reacting gases and gaseous products by volume is: CH_4 : O_2 : CO_2 1 : 2 : 1 Using the volume of O_2 reacted (24.0 cm^3): Volume of CH_4 reacted = 24.0 cm^3 O_2 × 1 volume CH_42 volumes O_2 = 12.0 cm^3 CH_4 This matches the initial volume of methane (12.0 cm^3), confirming that all methane reacted. Volume of CO_2 produced = 24.0 cm^3 O_2 × 1 volume CO_22 volumes O_2 = 12.0 cm^3 CO_2 Step 4: Verify the final volume. The final volume measured is the sum of the gaseous products and any unreacted gaseous reactants. Final volume = Volume of CO_2 produced + Volume of unused O_2 Final volume = 12.0 cm^3 + 24.0 cm^3 = 36.0 cm^3 This matches the given final volume of 36.0 cm^3. Step 5: Show the ratio of reacting volumes of gases and gaseous products formed. The reacting gases are CH_4 and O_2. The gaseous product is CO_2. Ratio = Volume of CH_4 reacted : Volume of O_2 reacted : Volume of CO_2 produced Ratio = 12.0 cm^3 : 24.0 cm^3 : 12.0 cm^3 Divide by the smallest volume (12.0 cm^3) to get the simplest whole number ratio: Ratio = (12.0)/(12.0) : (24.0)/(12.0) : (12.0)/(12.0) Ratio = 1 : 2 : 1 The ratio of reacting volume of methane to reacting volume of oxygen to gaseous carbon dioxide produced is 1:2:1. Got more? Send 'em