Understanding how to calculate the mass of a given number of moles of a chemical compound is a fundamental skill in chemistry. One specific question that often arises in this context is: what is the mass of 3.81 mol of PH3? This article provides a detailed, step-by-step guide to answering this question, ensuring clarity for students, educators, and chemistry enthusiasts. By exploring the molar mass of phosphine (PH3), the concept of moles, and the necessary calculations, we aim to deliver a comprehensive yet easy-to-read explanation. Let’s dive into solving what is the mass of 3.81 mol of PH3.
Introduction to Moles and Molar Mass
To address what is the mass of 3.81 mol of PH3, we first need to understand two key concepts: moles and molar mass. In chemistry, a mole is a unit that is used to measure the quantity of a material. One mole of any substance contains Avogadro’s number of particles, which is approximately 6.022 × 10²³ particles (atoms, molecules, or ions). The molar mass, expressed in grams per mole (g/mol), is the mass of one mole of a substance and is numerically equal to the substance’s molecular or atomic weight.
For PH3, or phosphine, a colorless, flammable gas used in various industrial applications, we need to determine its molar mass to calculate what is the mass of 3.81 mol of PH3. Phosphine consists of one phosphorus atom and three hydrogen atoms, so we’ll compute its molar mass by summing the atomic masses of these elements.
Step-by-Step Calculation of Molar Mass of PH3
To find what is the mass of 3.81 mol of PH3, we start by calculating the molar mass of PH3. The atomic masses of the elements involved, based on the periodic table, are:
- Phosphorus (P): 30.9738 g/mol (approximately 31.0 g/mol for simplicity in calculations).
- Hydrogen (H): 1.0079 g/mol (approximately 1.0 g/mol for simplicity).
Since PH3 has one phosphorus atom and three hydrogen atoms, the molar mass is calculated as follows:
- Mass of phosphorus: 1 × 31.0 g/mol = 31.0 g/mol.
- Mass of hydrogen: 3 × 1.0 g/mol = 3.0 g/mol.
- Total molar mass of PH3: 31.0 g/mol + 3.0 g/mol = 34.0 g/mol.
Thus, the molar mass of PH3 is 34.0 g/mol. This value is critical for determining what is the mass of 3.81 mol of PH3.
Formula for Calculating Mass from Moles
The relationship between mass, moles, and molar mass is given by the formula:
Mass equals the product of the number of moles and the molar mass.
To find what is the mass of 3.81 mol of PH3, we apply this formula, using the number of moles (3.81 mol) and the molar mass of PH3 (34.0 g/mol). Let’s perform the calculation step-by-step.
Calculating the Mass of 3.81 Mol of PH3
Now, let’s compute what is the mass of 3.81 mol of PH3:
[ \text{Mass} = 3.81 , \text{mol} \times 34.0 , \text{g/mol} ]
First, multiply 3.81 by 34.0:
[ 3.81 \times 34.0 = 129.54 ]
So, the mass is 129.54 grams. To ensure accuracy, let’s break down the multiplication:
- ( 3.81 \times 30 = 114.3 )
- ( 3.81 \times 4 = 15.24 )
- Total: ( 114.3 + 15.24 = 129.54 )
The units of moles cancel out, leaving grams as the unit of mass. Therefore, what is the mass of 3.81 mol of PH3? It is 129.54 grams.
Verifying the Calculation
To confirm our answer to what is the mass of 3.81 mol of PH3, let’s consider the precision of the given values. The number of moles (3.81) has three significant figures, and the molar mass (34.0 g/mol) also has three significant figures. Thus, the final answer should be reported with three significant figures:
[ 129.54 \approx 129.5 , \text{grams} ]
However, for simplicity and consistency with typical chemistry problems, we can round to 129.5 grams or even 130 grams if only two significant figures are required. For this article, we’ll use 129.54 grams to maintain precision in addressing what is the mass of 3.81 mol of PH3.
Practical Applications of PH3 and Mass Calculations
Understanding what is the mass of 3.81 mol of PH3 has practical implications. Phosphine is used in semiconductor manufacturing, as a fumigant in agriculture, and in chemical synthesis. Knowing the mass of a given number of moles helps chemists and engineers measure precise quantities for reactions or processes. For example, if a reaction requires 3.81 mol of PH3, knowing that this corresponds to 129.54 grams ensures accurate preparation.
Common Mistakes to Avoid
When calculating what is the mass of 3.81 mol of PH3, students often make errors, such as:
- Incorrect Molar Mass: Using outdated or incorrect atomic masses. Consistently consult a dependable periodic table.
- Unit Confusion: Forgetting to cancel units in the formula, leading to incorrect results.
- Significant Figures: Not adhering to the rules of significant figures, which can affect the precision of the answer.
By double-checking the molar mass and following the formula systematically, you can accurately determine what is the mass of 3.81 mol of PH3.
Why This Calculation Matters
The question what is the mass of 3.81 mol of PH3 is more than a textbook exercise. It reinforces the importance of stoichiometry, the branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions. Mastering such calculations prepares students for advanced topics like gas laws, reaction yields, and chemical kinetics.
Conclusion
In conclusion, calculating what is the mass of 3.81 mol of PH3 involves determining the molar mass of phosphine (34.0 g/mol) and applying the formula (\text{Mass} = \text{Moles} \times \text{Molar mass}). The result is 129.54 grams, a precise answer that demonstrates the power of stoichiometric calculations. Whether you’re a student tackling chemistry homework or a professional handling phosphine in an industrial setting, understanding what is the mass of 3.81 mol of PH3 equips you with essential skills. By following the steps outlined in this article, you can confidently solve similar problems and deepen your chemistry knowledge.
FAQs
1. What is the molar mass of PH3, and why is it important for calculating what is the mass of 3.81 mol of PH3?
The molar mass of PH3 is 34.0 g/mol, calculated by adding the atomic mass of one phosphorus (31.0 g/mol) and three hydrogens (3 × 1.0 g/mol). It’s crucial because it converts moles to grams in the formula for mass.
2. Can I use a different molar mass for PH3 to find what is the mass of 3.81 mol of PH3?
Using a different molar mass would lead to an incorrect result. Always use the standard atomic masses from the periodic table for accuracy.
3. How many significant figures should I use when answering what is the mass of 3.81 mol of PH3?
Since 3.81 has three significant figures and 34.0 has three, the answer (129.54 grams) should be reported with three significant figures, such as 129.5 grams.
4. What are the uses of PH3, and why might someone need to know what is the mass of 3.81 mol of PH3?
PH3 is used in semiconductor production and as a fumigant. Knowing its mass helps in preparing precise quantities for chemical reactions or industrial processes.
5. What happens if I make an error in calculating what is the mass of 3.81 mol of PH3?
Errors, such as incorrect molar mass or misapplying the formula, can lead to wrong measurements, affecting experiments or industrial applications. Double-check calculations to ensure accuracy.
