Question

Calculate the mass in grams of this unit cell. Submit an answer

with three significant figures. (Molar mass of tantalum = 180.95
g/mol)

Answer 1

To calculate the mass of the unit cell, multiply the molar mass of the compound by the number of moles. Divide the given mass of the compound by the molar mass to find the number of moles. Multiply the number of moles by the molar mass to find the mass of the unit cell.

Step-by-step explanation:

The mass of the unit cell can be calculated by multiplying the molar mass of tantalum (180.95 g/mol) by the number of moles of the compound. To find the number of moles, divide the given mass of the compound by the molar mass. The resulting mass in grams is equal to the number of moles multiplied by the molar mass. Therefore, the mass of the unit cell is determined by the molar mass of the compound and the number of moles.

Let's use an example. If the given mass of the compound is 0.25 g, divide it by the molar mass of tantalum (180.95 g/mol) to find the number of moles:

Number of moles = 0.25 g / 180.95 g/mol = 0.001381 moles

Finally, multiply the number of moles by the molar mass:

Mass of the unit cell = 0.001381 moles * 180.95 g/mol = 0.25 g

Answer 2

The mass of the unit cell is approximately
`\(6.02 * 10^(-22)\) g`.( three significant figures).

To calculate the mass of the unit cell, we first need to determine the number of moles of tantalum atoms in one unit cell. The mass of one mole of tantalum atoms (molar mass) is given as 180.95 g/mol.

The unit cell of a crystal structure often contains more than one atom. In the case of a body-centered cubic (BCC) unit cell, there are two atoms per unit cell.

The calculation is as follows:

1. Determine the number of moles of tantalum atoms in one unit cell:

`\[ \text{Moles of Ta atoms} = \frac{\text{Number of atoms per unit cell}}{\text{Avogadro's number}} \]`

For BCC, there are 2 atoms per unit cell.

`\[ \text{Moles of Ta atoms} = \frac{2}{6.022 * 10^(23) \, \text{mol}^(-1)} \]`

2. Calculate the mass of the unit cell:

`\[ \text{Mass of unit cell} = \text{Moles of Ta atoms} * \text{Molar mass of tantalum} \]`

`\[ \text{Mass of unit cell} = \left(\frac{2}{6.022 * 10^(23) \, \text{mol}^(-1)}\right) * 180.95 \, \text{g/mol} \]`

Let's calculate the mass of the unit cell using the given expression:

`\[ \text{Mass of unit cell} = \left(\frac{2}{6.022 * 10^(23) \, \text{mol}^(-1)}\right) * 180.95 \, \text{g/mol} \]`

`\[ \text{Mass of unit cell} = (2 * 180.95)/(6.022 * 10^(23)) \, \text{g} \]`

`\[ \text{Mass of unit cell} \approx (361.90)/(6.022 * 10^(23)) \, \text{g} \]`

Now, calculate this expression:

`\[ \text{Mass of unit cell} \approx 6.018 * 10^(-22) \, \text{g} \]`

Rounding to three significant figures, the mass of the unit cell is approximately
`\(6.02 * 10^(-22)\) g`.