What is the volume V of a sample of 3.40mol of copper? The atomic mass of copper (Cu) is 63.5 g/mol, and the density of copper is 8.92×10^3kg/m^3?
mass = volume x density
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To find the volume of a sample of copper, we need to use the given mass and density. Here's how to calculate it step-by-step:
Step 1: Convert moles of copper to grams
Since the atomic mass of copper is 63.5 g/mol, we can use this conversion factor to find the mass of copper:
1 mol Cu = 63.5 g Cu
Given: 3.40 mol Cu
By multiplying the given number of moles by the molar mass, we can convert moles to grams:
3.40 mol Cu × 63.5 g Cu/mol = 215.9 g Cu
Step 2: Convert grams to kilograms
Since the density of copper is given in kg/m^3, we need to convert the mass of copper from grams to kilograms:
215.9 g Cu × (1 kg / 1000 g) = 0.2159 kg Cu
Step 3: Calculate the volume
Using the formula for density: density = mass / volume, we can rearrange the equation to solve for volume:
volume = mass / density
Substituting the given values into the formula:
volume = 0.2159 kg Cu / 8.92×10^3kg/m^3
Step 4: Calculate the value
To calculate the volume, we divide the mass by the density:
volume ≈ 0.024 m^3
Therefore, the volume of a sample of 3.40 mol of copper is approximately 0.024 cubic meters (m^3).
To calculate the volume of a sample of copper, we need to use the number of moles, the molar mass, and the density of copper. Here's how you can do it:
1. Determine the mass of the sample:
Mass (m) = Number of moles (n) × Molar mass (M)
Mass (m) = 3.40 mol × 63.5 g/mol
Mass (m) = 215.9 g
2. Convert the mass from grams to kilograms:
Mass (m) = 215.9 g ÷ 1000 = 0.2159 kg
3. Use the density formula to find the volume:
Density (ρ) = Mass (m) / Volume (V)
Volume (V) = Mass (m) / Density (ρ)
Volume (V) = 0.2159 kg ÷ 8.92 × 10^3 kg/m^3
Now let's calculate the volume:
Volume (V) = 0.024 m^3
Therefore, the volume of the sample of 3.40 mol of copper is 0.024 cubic meters.