Question: 1. How many kilograms of Magnesium are in 178.65mol? 1 mole of Magnesium is 24.305g.
2. If the density of Magnesium is 1.738 gram per cubic centimeter, what is its volume in L (given the same sample in #1).
1. **Problem 1: Calculate the mass of Magnesium in kilograms given moles**
We are given:
- Number of moles of Magnesium, $n = 178.65$ mol
- Molar mass of Magnesium, $M = 24.305$ g/mol
**Formula:**
$$\text{Mass} = n \times M$$
**Step 1:** Calculate the mass in grams:
$$\text{Mass} = 178.65 \times 24.305 = 4341.23 \text{ g}$$
**Step 2:** Convert grams to kilograms:
$$\text{Mass in kg} = \frac{4341.23}{1000} = 4.34123 \text{ kg}$$
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2. **Problem 2: Calculate the volume of Magnesium in liters given its density and mass**
We are given:
- Density, $\rho = 1.738$ g/cm$^3$
- Mass from problem 1, $m = 4341.23$ g
**Formula:**
$$\text{Volume} = \frac{\text{Mass}}{\text{Density}}$$
**Step 1:** Calculate volume in cm$^3$:
$$V = \frac{4341.23}{1.738} = 2496.43 \text{ cm}^3$$
**Step 2:** Convert cm$^3$ to liters (1 L = 1000 cm$^3$):
$$V = \frac{2496.43}{1000} = 2.49643 \text{ L}$$
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**Final answers:**
- Mass of Magnesium = $4.341$ kg (rounded to 3 decimal places)
- Volume of Magnesium = $2.496$ L (rounded to 3 decimal places)