N₂ content in a urea sample was found to be only 42%. What is the actual urea content of the sample ? (molecular weight of urea = 60)

ANS:B - 90%

To find the actual urea content of the sample, we need to consider that the nitrogen content in urea (CO(NH2)2) is 46.65% by mass. Therefore, if the nitrogen content in the sample is 42%, we can calculate the proportion of urea in the sample. Let's denote:

• 𝑥x as the mass of the urea in the sample (in grams)
• 0.42𝑥0.42x as the mass of nitrogen in the sample (since 42% of the sample is nitrogen)
• 6060 as the molecular weight of urea (in g/mol)

We know that the mass of nitrogen in urea is 46.65% of its total mass. So, we can set up the equation: mass of nitrogen in ureamass of urea=0.4665mass of ureamass of nitrogen in urea​=0.4665 0.42𝑥𝑥=0.4665x0.42x​=0.4665 Solving for 𝑥x: 0.42𝑥=0.4665𝑥0.42x=0.4665x 0.4665𝑥−0.42𝑥=00.4665x−0.42x=0 0.0465𝑥=00.0465x=0 𝑥=00.0465x=0.04650​ 𝑥=0x=0 This result suggests that there is no urea in the sample. However, this is not possible because urea is present in the sample. This means we made a mistake in the calculations. The mistake lies in the assumption that 100% of the urea's mass is contributed by nitrogen. In reality, only 46.65% of urea's mass comes from nitrogen. So, let's correct the calculation: Actual mass of urea=Mass of nitrogen in samplePercentage of nitrogen in ureaActual mass of urea=Percentage of nitrogen in ureaMass of nitrogen in sample​ Actual mass of urea=0.42𝑥0.4665Actual mass of urea=0.46650.42x​ Actual mass of urea=0.420.4665𝑥Actual mass of urea=0.46650.42​x Actual mass of urea=0.9008𝑥Actual mass of urea=0.9008x This tells us that the actual mass of urea in the sample is approximately 0.9008 times the total mass of the sample. Now, if 42% of the sample is nitrogen and 90.08% of the sample is urea, the remaining mass of the sample must be other components or impurities. So, the actual urea content of the sample is 90.08%90.08%. Therefore, the correct answer is 90%90%.