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Chapter 5: Problem 88

Nickel forms a gaseous compound of the formula \(\mathrm{Ni}(\mathrm{CO})_{x} .\) What is the value of \(x\) given the fact that under the same conditions of temperature and pressure, methane \(\left(\mathrm{CH}_{4}\right)\) effuses 3.3 times faster than the compound?

Short Answer

Expert verified
After calculating, the value of \(x\) is found to be approximately 4. Hence, the formula of the compound is \(Ni(CO)_4\).

Step by step solution

01

Write down the Graham's law of effusion

Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be expressed as \(\frac{r1}{r2} = \sqrt{\frac{M2}{M1}}\) where \(r1\) and \(r2\) are the rates of effusion of gas 1 and gas 2, and \(M1\) and \(M2\) are their molar masses.
02

Plug given values in the formula

Given that methane (\(CH4\), molar mass \(16.04g/mol\)) effuses 3.3 times faster than the unknown compound, this implies \(\frac{r_{CH4}}{r_{Ni(CO)_x}} = 3.3\) and it also implies \(\frac{r_{CH4}}{r_{Ni(CO)_x}} = \sqrt{\frac{M_{Ni(CO)_x}}{M_{CH4}}}\). Thus, we can set \(3.3 = \sqrt{\frac{M_{Ni(CO)_x}}{16.04}}\).
03

Calculate molar mass of unknown compound

Solving the equation for \(M_{Ni(CO)_x}\), it gives \(M_{Ni(CO)_x} = (3.3)^2 * 16.04= 173.23g/mol\). This is the molar mass of the unknown compound.
04

Determine the value of x

The molecular formula for the compound is \(Ni(CO)_x\), where x is what we need to determine. The number of carbonyl groups (\(CO\)) of a molecue of \(Ni(CO)_x\) will be mass of \(Ni(CO)_x\)- mass of Ni divided by mass of \(CO\). Nickel (Ni) has a molar mass of \(58.69g/mol\) and Carbon monoxide (\(CO\)) has a molar mass of \(28.01g/mol\). Thus, the formula is \(x = \frac{173.23 - 58.69}{28.01}\).

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Most popular questions from this chapter

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) can be obtained by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right) .\) (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains \(0.340 \mathrm{~L}\) of the gas at \(718 \mathrm{mmHg}\) and \(24^{\circ} \mathrm{C}\). If the gas weighs \(0.580 \mathrm{~g},\) calculate the value of the gas constant.

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures \(15.2 \mathrm{~m}\) long, \(6.6 \mathrm{~m}\) wide, and \(2.4 \mathrm{~m}\) high. (a) Calculate the mass of mercury vapor (in grams) in the room at \(20^{\circ} \mathrm{C}\). The vapor pressure of mercury at \(20^{\circ} \mathrm{C}\) is \(1.7 \times 10^{-6} \mathrm{~atm} .\) (b) Does the concentration of mercury vapor exceed the air quality regulation of \(0.050 \mathrm{mg} \mathrm{Hg} / \mathrm{m}^{3}\) of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) At temperatures above \(43^{\circ} \mathrm{C}\), the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

State Dalton's law of partial pressures and explain what mole fraction is. Does mole fraction have units?

A gas evolved during the fermentation of glucose (wine making) has a volume of \(0.78 \mathrm{~L}\) at \(20.1^{\circ} \mathrm{C}\) and 1.00 atm. What was the volume of this gas at the fermentation temperature of \(36.5^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) pressure?
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