How to Calculate the Amount of Niobium (III) Carbide Produced from Coke

How many kilograms of niobium (III) carbide can be prepared from 151 kg of coke that is 44.7% carbon?

By applying stoichiometry principles, it is calculated that under ideal conditions, approximately 770.92 kg of niobium (III) carbide can be produced from 151 kg of coke that consists of 44.7% carbon.

Understanding Stoichiometry in Chemical Reactions

Stoichiometry is a crucial concept in chemistry that involves calculating the quantitative relationships between reactants and products in chemical reactions. In this particular scenario, we are tasked with determining the amount of niobium (III) carbide that can be produced from a given quantity of coke containing a specific percentage of carbon. Firstly, let's break down the given information. We start with 151 kg of coke that is composed of 44.7% carbon. To find the amount of carbon in kilograms, we multiply the total mass of coke by the percentage of carbon:

Mass of carbon in coke: 151 kg * 0.447 = 67.497 kg

Next, we convert this mass of carbon to moles by utilizing the molar mass of carbon which is approximately 12.01 g/mol:

Number of moles of carbon: 67,497 g / 12.01 g/mol = 5620.32 mol

Now, we refer to the balanced chemical equation provided: 4 Nb + 3 C → Nb4C3 In this equation, the mole ratio of carbon to Nb4C3 is 3:1. By applying this ratio, we calculate the number of moles of Nb4C3 that can be produced: Moled of Nb4C3: 5620.32 mol / 3 = 1873.44 mol To determine the final mass of niobium (III) carbide in kilograms, we convert the number of moles of Nb4C3 back to grams and then to kilograms using the molar mass of Nb4C3: Mass of niobium (III) carbide: 1873.44 mol * 411.64 g/mol = 770918.682 g or 770.92 kg Therefore, through the principles of stoichiometry, we establish that around 770.92 kg of niobium (III) carbide can theoretically be generated from 151 kg of coke containing 44.7% carbon.
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