B. Nuts and Bolts Stoichiometry and Dozens of Hardware Pieces. Consider this reaction in terms of dozens of hardware pieces: B + 3N = BN3 One dozen bolts combines with three dozen nuts to make one dozen BN3.
Use the masses from above to determine the mass of a dozen of each. Even though simple, show work! Round each to 3 significant digits.
bolt (B) mass of one dozen bolts (B) =
nut (N) mass of one dozen nuts (N) =
bolt/nut combination (BN3)
mass of one dozen combinations (BN3) =
Solve IN TERMS OF DOZENS of hardware pieces. These are solved exactly as those above, except the unit of dozen and the masses for dozens of pieces are used instead of individual pieces and the masses of single pieces.
4. What mass of bolts (B) is needed to combine with 224.4 g of nuts (N)? Hint: start with determining the number of dozens nuts of available by utilizing the mass of a dozen nuts above. The next step is to use the equation, assuming the coefficients are dozens...
5. What mass of BN3 can be made from 673.2 g nuts N?
6. What mass of nuts (N) is needed to combine with 979.2 g bolts (B)?
To solve these problems, we need to first determine the mass of one dozen bolts, one dozen nuts, and one dozen bolt/nut combinations (BN3) using the given information.
1. Mass of one dozen bolts (B):
From the information given, one dozen bolts combines with three dozen nuts to make one dozen BN3. This means that the ratio of bolts to BN3 is 1:1. Therefore, the mass of one dozen bolts will be equal to the mass of one dozen BN3.
2. Mass of one dozen nuts (N):
Since one dozen bolts combines with three dozen nuts to make one dozen BN3, the ratio of nuts to BN3 is 3:1. Therefore, the mass of one dozen nuts will be three times the mass of one dozen BN3.
3. Mass of one dozen BN3:
From the equation, we see that one dozen BN3 is formed when one dozen bolts combines with three dozen nuts. This means that the mass of one dozen BN3 will be the sum of the masses of one dozen bolts and three dozen nuts.
Let's calculate the masses:
1. Mass of one dozen bolts (B):
Start with the mass of one dozen BN3 (we'll use 'x' to represent it):
x = mass of one dozen BN3
2. Mass of one dozen nuts (N):
Since the mass of one dozen nuts is three times the mass of one dozen BN3, we have:
3x = mass of one dozen nuts
3. Mass of one dozen BN3:
Given that one dozen BN3 is formed by combining one dozen bolts and three dozen nuts, we can write:
1x + 3x = mass of one dozen BN3
4x = mass of one dozen BN3
Now, we can solve for the masses.
1. Mass of one dozen bolts (B):
From the equation 4x = mass of one dozen BN3, we know that the mass of one dozen bolts is equal to the mass of one dozen BN3. Therefore:
Mass of one dozen bolts (B) = mass of one dozen BN3.
2. Mass of one dozen nuts (N):
From the equation 3x = mass of one dozen nuts, we know that the mass of one dozen nuts is three times the mass of one dozen BN3. Therefore:
Mass of one dozen nuts (N) = 3 * (mass of one dozen BN3).
3. Mass of one dozen BN3:
From the equation 4x = mass of one dozen BN3, we can solve for x:
x = mass of one dozen BN3 / 4.
We have now determined the masses of one dozen bolts, one dozen nuts, and one dozen BN3 using the given information. Now we can move on to solving the specific problems.
4. Mass of bolts (B) needed to combine with 224.4 g of nuts (N):
First, determine the number of dozens of nuts using the mass of one dozen nuts:
Number of dozens nuts = 224.4 g / (mass of one dozen nuts).
Next, we use the equation B + 3N = BN3, assuming coefficients are in dozens:
Mass of bolts (B) = Number of dozens nuts * 1 (coefficient of B) * mass of one dozen bolts.
5. Mass of BN3 that can be made from 673.2 g of nuts (N):
First, determine the number of dozens of nuts using the mass of one dozen nuts:
Number of dozens nuts = 673.2 g / (mass of one dozen nuts).
Next, we use the equation B + 3N = BN3, assuming coefficients are in dozens:
Mass of BN3 = Number of dozens nuts * 1 (coefficient of BN3) * mass of one dozen BN3.
6. Mass of nuts (N) needed to combine with 979.2 g of bolts (B):
First, determine the number of dozens of bolts using the mass of one dozen bolts:
Number of dozens bolts = 979.2 g / (mass of one dozen bolts).
Next, we use the equation B + 3N = BN3, assuming coefficients are in dozens:
Mass of nuts (N) = Number of dozens bolts * 3 (coefficient of N) * mass of one dozen nuts.