Use the 5-step method and be sure to include units where appropriate. Round your answers to the correct number of significant digits.
Mass m
Density = -------------- or D = ------
Volume v
Adjust the density formula and solve the problems below:
m
D = ------- Original Formula
v
Adjust the formula for the unknown m =
1. The density of silver is 110.49 g/cm3. If a sample of pure silver has a volume of 112.993 cm3, what would the mass?
2. How many grams of tin would occupy 15.5 L, if it has a density of 17.265 g/cm3?(hint 1L=1000cm3)
3. What is the mass of a 1350 cm3 sample of pure silicon with a density of 21.336 g/cm3?
To solve each problem using the 5-step method, follow these steps:
Step 1: Identify the given information and the unknown quantity
1. For problem 1:
Given information:
Density of silver = 110.49 g/cm^3
Volume = 112.993 cm^3
Unknown: Mass (m)
2. For problem 2:
Given information:
Density of tin = 17.265 g/cm^3
Volume = 15.5 L
Unknown: Mass (m)
3. For problem 3:
Given information:
Density of silicon = 21.336 g/cm^3
Volume = 1350 cm^3
Unknown: Mass (m)
Step 2: Write down the formula
The formula for density is:
Density (D) = Mass (m) / Volume (v)
Step 3: Adjust the formula for the unknown quantity
In each problem, we need to solve for mass (m). Rearrange the formula to isolate mass:
m = D * v
Step 4: Plug in the values and solve the equation
1. For problem 1:
Given:
D = 110.49 g/cm^3
v = 112.993 cm^3
Plugging in the values:
m = 110.49 g/cm^3 * 112.993 cm^3
Calculating:
m = 12475.44557 g
2. For problem 2:
Given:
D = 17.265 g/cm^3
v = 15.5 L (1 L = 1000 cm^3, so v = 15.5 * 1000 cm^3)
Plugging in the values:
m = 17.265 g/cm^3 * (15.5 * 1000) cm^3
Calculating:
m = 267,412.5 g
3. For problem 3:
Given:
D = 21.336 g/cm^3
v = 1350 cm^3
Plugging in the values:
m = 21.336 g/cm^3 * 1350 cm^3
Calculating:
m = 28,809.6 g
Step 5: Round the answer to the correct number of significant digits
The number of significant digits in each problem was not specified, so we'll round our answers to three significant digits:
1. For problem 1:
m = 12,500 g (rounded to three significant digits)
2. For problem 2:
m = 268,000 g (rounded to three significant digits)
3. For problem 3:
m = 28,800 g (rounded to three significant digits)
Note: Make sure to include the appropriate units in your final answer.