What is the mass of $1.450 mol Cd _3 N_2$?
A. 124.2 g
B. 234.7 g
C. 529.6 g
D. 738.9 g
Answer (2)
Calculate the molar mass of C d 3 N 2 : 3 ( 112.41 ) + 2 ( 14.01 ) = 365.25 g / m o l .
Multiply the number of moles by the molar mass: 1.450 m o l × 365.25 g / m o l = 529.6125 g .
Round the result to one decimal place: 529.6 g .
The mass of 1.450 mol C d 3 N 2 is 529.6 g .
Explanation
Problem Analysis We are asked to find the mass of 1.450 moles of Cadmium Nitride ( C d 3 N 2 ). To do this, we will first calculate the molar mass of C d 3 N 2 and then multiply it by the number of moles.
Molar Masses of Elements The molar mass of a compound is the sum of the atomic masses of each element in the compound, multiplied by the number of atoms of that element. The molar mass of Cadmium (Cd) is 112.41 g/mol, and the molar mass of Nitrogen (N) is 14.01 g/mol.
Calculating Molar Mass of Cd3N2 Now, we calculate the molar mass of C d 3 N 2 :
M o l a r , M a ss , o f C d 3 N 2 = 3 × ( M o l a r M a ss o f C d ) + 2 × ( M o l a r M a ss o f N ) M o l a r , M a ss , o f C d 3 N 2 = 3 × ( 112.41 g / m o l ) + 2 × ( 14.01 g / m o l ) M o l a r , M a ss , o f C d 3 N 2 = 337.23 g / m o l + 28.02 g / m o l M o l a r , M a ss , o f C d 3 N 2 = 365.25 g / m o l
Calculating Mass of Cd3N2 Now that we have the molar mass of C d 3 N 2 , we can calculate the mass of 1.450 moles of C d 3 N 2 :
M a ss = ( N u mb er o f M o l es ) × ( M o l a r M a ss ) M a ss = 1.450 m o l × 365.25 g / m o l M a ss = 529.6125 g Rounding to one decimal place, we get 529.6 g.
Final Answer Therefore, the mass of 1.450 mol of C d 3 N 2 is 529.6 g.
Examples
Understanding molar mass and its relationship to mass is crucial in various fields. For instance, in pharmaceuticals, accurately calculating the mass of compounds is essential for drug formulation. If a medication requires 1.450 moles of C d 3 N 2 as an active ingredient, knowing its molar mass allows pharmacists to precisely measure out 529.6 g, ensuring the correct dosage and effectiveness of the drug. This principle extends to other areas like environmental science, where calculating the mass of pollutants helps in assessing environmental impact and designing remediation strategies.
The mass of 1.450 moles of Cadmium Nitride (Cd3N2) is 529.6 g, calculated using its molar mass. Therefore, the correct answer is option C. 529.6 g.
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