Question

homework: mixed mole problems
now you try! remember to show all work and report your answers with the correct number of figures and the correct units! use your mole map!!

1. how many grams are in 14.05 mol silver?
2. how many moles are in 895 g of ba(oh)₂?
3. at stp, neon is a gas. how many moles are found in 0.317 l?
4. how many liters are in 44.3 moles of helium gas at stp?

Explanation:

Step1: Calculate the mass of silver

The molar mass of silver (Ag) is \(M = 107.87\space g/mol\).
We use the formula \(m=n\times M\), where \(n = 14.05\space mol\) and \(M=107.87\space g/mol\).

$$m = 14.05\times107.87$$

$$m=14.05\times(100 + 7+0.87)$$

$$m=14.05\times100+14.05\times7 + 14.05\times0.87$$

$$m = 1405+98.35+12.2235$$

$$m=1515.5735\approx1516\space g$$

Step2: Calculate the molar mass of \(Ba(OH)_2\)

The molar mass of \(Ba\) is \(M_{Ba}=137.33\space g/mol\), the molar mass of \(O\) is \(M_O = 16\space g/mol\), and the molar mass of \(H\) is \(M_H=1.01\space g/mol\).

$$M_{Ba(OH)_2}=M_{Ba}+2\times(M_O + M_H)$$

$$M_{Ba(OH)_2}=137.33+2\times(16 + 1.01)$$

$$M_{Ba(OH)_2}=137.33+2\times17.01$$

$$M_{Ba(OH)_2}=137.33 + 34.02=171.35\space g/mol$$

We use the formula \(n=\frac{m}{M}\), where \(m = 895\space g\) and \(M = 171.35\space g/mol\)

$$n=\frac{895}{171.35}\approx5.22\space mol$$

Step3: Calculate the number of moles of neon at STP

At STP (Standard Temperature and Pressure), \(V_m=22.4\space L/mol\).
We use the formula \(n=\frac{V}{V_m}\), where \(V = 0.317\space L\) and \(V_m = 22.4\space L/mol\)

$$n=\frac{0.317}{22.4}\approx0.0141\space mol$$

Step4: Calculate the volume of helium gas at STP

At STP, \(V_m = 22.4\space L/mol\).
We use the formula \(V=n\times V_m\), where \(n = 44.3\space mol\) and \(V_m=22.4\space L/mol\)

$$V=44.3\times22.4$$

$$V=(40 + 4+0.3)\times22.4$$

$$V=40\times22.4+4\times22.4+0.3\times22.4$$

$$V = 896+89.6+6.72$$

$$V=992.32\approx992\space L$$

Answer:

1. \(1516\space g\)
2. \(5.22\space mol\)
3. \(0.0141\space mol\)
4. \(992\space L\)