Question

How many grams of sih4 contain 8.23 × 1022 atoms of hydrogen?

Answer 1

To find the grams of SiH4 containing 8.23 × 10^22 atoms of hydrogen, calculate the molar mass of SiH4 and use conversion factors to relate the number of hydrogen atoms to grams of SiH4.

Step-by-step explanation:

To determine the number of grams of SiH4 that contain 8.23 × 10^22 atoms of hydrogen, we need to use the molar mass and conversion factors.

1. Calculate the molar mass of SiH4 (silane) by summing the atomic masses of each element in the compound: 1.0079 g/mol for hydrogen and 28.0855 g/mol for silicon. The molar mass of SiH4 is 32.1074 g/mol.

2. Use the conversion factors to relate the number of hydrogen atoms to grams of SiH4. There are 4 hydrogen atoms in 1 molecule of SiH4. Therefore, we can set up the following proportion: (8.23 × 10^22 atoms of hydrogen) / (6.022 x 10^23 atoms/mol) = x grams of SiH4, where x is the unknown.

3. Solve for x by cross-multiplying and dividing: x = (32.1074 g/mol) * (8.23 × 10^22 atoms of hydrogen) / (6.022 x 10^23 atoms/mol).

Calculating this expression gives an answer of x = 0.4407 grams of SiH4.

Answer 2

To calculate the grams of SiH4 containing a specific number of hydrogen atoms, you need to calculate the molar mass of SiH4 and use it to convert moles to grams.

Step-by-step explanation:

To determine the number of grams of SiH4 that contain 8.23 × 10²² atoms of hydrogen, we need to first calculate the molar mass of SiH4. Silicon (Si) has a molar mass of 28.09 g/mol and hydrogen (H) has a molar mass of 1.01 g/mol. SiH4 consists of 1 silicon atom and 4 hydrogen atoms. Therefore, the molar mass of SiH4 is 28.09 g/mol + 4(1.01 g/mol) = 32.13 g/mol.

Next, we can calculate the number of moles of SiH4 that contain 8.23 × 10²² atoms of hydrogen by dividing the given number of atoms by Avogadro's number (6.022 × 10²³ atoms/mol):

(8.23 × 10²² atoms) / (6.022 × 10²³ atoms/mol) = 0.13666 mol

Finally, we can use the molar mass of SiH4 to convert moles to grams:

(0.13666 mol) × (32.13 g/mol) = 4.39 grams of SiH4