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In-s [12.5K]
3 years ago
11

Based on the ideal gas law, there is a simple equivalency that exists between the amount of gas and the volume it occupies. at s

tandard temperature and pressure (stp; 273.15 k and 1 atm, respectively), one mole of gas occupies 22.4 l of volume. what mass of methanol (ch3oh) could you form if you reacted 5.86 l of a gas mixture (at stp) that contains an equal number of carbon monoxide (co) and hydrogen gas (h2) molecules?
Chemistry
1 answer:
nordsb [41]3 years ago
4 0
<span>2.10 grams. The balanced equation for the reaction is CO + 2H2 ==> CH3OH The key thing to take from this equation is that it takes 2 hydrogen molecules per carbon monoxide molecule for this reaction. And since we've been given an equal number of molecules for each reactant, the limiting reactant will be hydrogen. We can effectively claim that we have 5.86/2 = 2.93 l of hydrogen and an excess of CO to consume all of the hydrogen. So the number of moles of hydrogen gas we have is: 2.93 l / 22.4 l/mol = 0.130803571 mol And since it takes 2 moles of hydrogen gas to make 1 mole of methanol, divide by 2, getting. 0.130803571 mol / 2 = 0.065401786 mol Now we just need to multiply the number of moles of methanol by its molar mass. First lookup the atomic weights involved. Atomic weight carbon = 12.0107 g/mol Atomic weight hydrogen = 1.00794 g/mol Atomic weight oxygen = 15.999 g/mol Molar mass CH3OH = 12.0107 + 4 * 1.00794 + 15.999 = 32.04146 g/mol So the mass produced is 32.04146 g/mol * 0.065401786 mol = 2.095568701 g And of course, properly round the answer to 3 significant digits, giving 2.10 grams.</span>
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(a) Compute the radius r of an impurity atom that will just fit into an FCC octahedral site in terms of the atomic radius R of t
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Answer:

a

The radius of an impurity atom occupying FCC octahedral site is 0.414{\rm{R}}

b

The radius of an impurity atom occupying FCC tetrahedral site is 0.225{\rm{R}} .

Explanation:

In order to get a better understanding of the solution we need to understand that the concept used to solve this question is based on the voids present in a unit cell. Looking at the fundamentals

An impurity atom in a unit cell occupies the void spaces. In FCC type of structure, there are two types of voids present. First, an octahedral void is a hole created when six spheres touch each other usually placed at the body center. On the other hand, a tetrahedral void is generated when four spheres touch each other and is placed along the body diagonal.

Step 1 of 2

(1)

The position of an atom that fits in the octahedral site with radius \left( r \right)is as shown in the first uploaded image.

In the above diagram, R is the radius of atom and a is the edge length of the unit cell.

The radius of the impurity is as follows:

2r=a-2R------(A)

The relation between radius of atom and edge length is calculated using Pythagoras Theorem is shown as follows:

Consider \Delta {\rm{XYZ}} as follows:

(XY)^ 2 =(YZ) ^2 +(XZ)^2

Substitute XY as{\rm{R}} + 2{\rm{R + R}} and {\rm{YZ}} as a and {\rm{ZX}} as a in above equation as follows:

(R+2R+R) ^2 =a ^2 +a^ 2\\16R ^2 =2a^ 2\\ a =2\sqrt{2R}

Substitute value of aa in equation (A) as follows:

r= \frac{2\sqrt{2}R -2R }{2} \\ =\sqrt{2} -1R\\ = 0.414R

The radius of an impurity atom occupying FCC octahedral site is 0.414{\rm{R}}

Note

An impure atom occupies the octahedral site, the relation between the radius of atom, edge length of unit cell and impure atom is calculated. The relation between the edge length and radius of atom is calculated using Pythagoras Theorem. This further enables in finding the radius of an impure atom.  

Step 2 of 2

(2)

The impure atom in FCC tetrahedral site is present at the body diagonal.

The position of an atom that fits in the octahedral site with radius rr is shown on the second uploaded image :

In the above diagram, R is the radius of atom and a is the edge length of the unit cell.

The body diagonal is represented by AD.

The relation between the radius of impurity, radius of atom and body diagonal is shown as follows:

AD=2R+2r----(B)

   In    \Delta {\rm{ABC}},

(AB) ^2 =(AC) ^2 +(BC) ^2

For calculation of AD, AB is determined using Pythagoras theorem.

Substitute {\rm{AC}} as a and {\rm{BC}} as a in above equation as follows:

(AB) ^2 =a ^2 +a ^2

AB= \sqrt{2a} ----(1)

Also,

AB=2R

Substitute value of 2{\rm{R}} for {\rm{AB}} in equation (1) as follows:

2R= \sqrt{2} aa = \sqrt{2} R

Therefore, the length of body diagonal is calculated using Pythagoras Theorem in \Delta {\rm{ABD}} as follows:

(AD) ^2 =(AB) ^2 +(BD)^2

Substitute {\rm{AB}} as \sqrt 2a   and {\rm{BD}} as a in above equation as follows:

(AD) ^2 =( \sqrt 2a) ^2 +(a) ^2 AD= \sqrt3a

For calculation of radius of an impure atom in FCC tetrahedral site,

Substitute value of AD in equation (B) as follows:

\sqrt 3a=2R+2r

Substitute a as \sqrt 2{\rm{R}} in above equation as follows:

( \sqrt3 )( \sqrt2 )R=2R+2r\\\\

r = \frac{2.4494R-2R}{2}\\

=0.2247R

\approx 0.225R

The radius of an impurity atom occupying FCC tetrahedral site is 0.225{\rm{R}} .

Note

An impure atom occupies the tetrahedral site, the relation between the radius of atom, edge length of unit cell and impure atom is calculated. The length of body diagonal is calculated using Pythagoras Theorem. The body diagonal is equal to the sum of the radii of two atoms. This helps in determining the relation between the radius of impure atom and radius of atom present in the unit cell.

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Balance the equation <br> NaOH + CH3COOH
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NaOH + CH3COOH -> CH3COONa + H20

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