What volume in $dm^3$ of oxygen at STP is required to convert 60 g of carbon completely into carbon (IV) oxide? $[C = 12, O = 16$, molar volume $= 22.4 dm^3]$
Answer (2)
Write the balanced chemical equation: C + O 2 → C O 2 .
Calculate moles of carbon: m o l e s C = 12 60 = 5 moles.
Determine moles of oxygen: m o l e s O 2 = m o l e s C = 5 moles.
Calculate volume of oxygen at s.t.p.: v o l u m e O 2 = 5 × 22.4 = 112.0 d m 3 . The final answer is 112.0
Explanation
Problem Analysis We are asked to find the volume of oxygen at standard temperature and pressure (s.t.p.) required to completely convert 60g of carbon into carbon (IV) oxide, which is C O 2 . We are given the molar volume at s.t.p. as 22.4 d m 3 , the atomic mass of carbon as 12, and the atomic mass of oxygen as 16.
Balanced Chemical Equation First, let's write the balanced chemical equation for the reaction between carbon and oxygen: C + O 2 → C O 2
Moles of Carbon Next, we calculate the number of moles of carbon used in the reaction. The formula to calculate moles is: m o l es = a t o mi c ma ss ma ss So, the number of moles of carbon is: m o l e s C = 12 g / m o l 60 g = 5 m o l es
Moles of Oxygen From the balanced chemical equation, we see that 1 mole of carbon reacts with 1 mole of oxygen ( O 2 ) to produce 1 mole of carbon dioxide ( C O 2 ). Therefore, the number of moles of oxygen required is equal to the number of moles of carbon.
Calculating Moles of Oxygen m o l e s O 2 = m o l e s C = 5 m o l es
Calculating Volume of Oxygen Now, we calculate the volume of oxygen at s.t.p. We know that the molar volume at s.t.p. is 22.4 d m 3 / m o l . The formula to calculate volume is: v o l u m e = m o l es × m o l a r v o l u m e So, the volume of oxygen is: v o l u m e O 2 = 5 m o l es × 22.4 d m 3 / m o l = 112.0 d m 3
Final Answer Therefore, the volume of oxygen required to convert 60g of carbon completely into carbon (IV) oxide at s.t.p. is 112.0 d m 3 .
Examples
This concept is crucial in various real-world applications, such as understanding combustion processes in engines, calculating the amount of oxygen needed for industrial processes like steel production, and determining the efficiency of carbon-based fuels. For instance, knowing the precise amount of oxygen required to burn a specific amount of fuel ensures complete combustion, maximizing energy output and minimizing harmful emissions. This principle is also vital in environmental science for assessing air quality and managing pollution.
To convert 60 g of carbon into carbon (IV) oxide at STP, 112.0 dm³ of oxygen is needed. This is calculated by determining the moles of carbon and using the molar volume of oxygen at STP. Using the balanced chemical equation, we find that 5 moles of oxygen are required, which corresponds to a volume of 112.0 dm³.
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