The dipole moment (μ) of HBr (a polar covalent molecule) is 0.851D (debye), and its percent ionic character is 12.6% . Estimate the bond length of the H−Br bond in picometers.
Notes for conversion:
1D= 3.34*10^-30 C*m & Q= 1.6*10^-19 C
The equation we will be using is μ=Q*r
-we need to rearrange this equation to solve for the bond length (r) making the equation now: r=μ/Q
The 0.851D needs to be converted to C*m. So we make a ratio now and multiply 0.851D=3.34*10^-30 C*m/ 1 D = 2.84*10^-30 C*m
(multiply 0.851 times 3.34*10^-30)
We need to also change out the Q (since it is in percent form to the actual amount) 100% Q= 1.6*10^-19 C
.126(which was 12.6%) times 1.6*10^-19 = 2.02*10^-20 C
now we can solve with our μ (2.84*10^-30) and Q (2.02*10^-20) using our equation r=μ/Q which will equal 1.41*10^-10 m
we need to make this into picometers now. 1m= 10^12pm
= 1.41*10^-10m * 10^12pm/1m = 141 pm
(if you need to answer this in 3 sig figs it is 14*10^1 pm)
To estimate the bond length of the H−Br bond in picometers, we can use the relationship between dipole moment and percent ionic character.
First, let's understand the concept of percent ionic character. In a covalent bond, electrons are shared between atoms. However, if there is a significant difference in electronegativity between the two atoms, the electron distribution becomes uneven, resulting in a polar covalent bond. The percent ionic character quantifies the extent to which a bond behaves like an ionic bond.
To estimate the bond length, we can use the equation:
μ = (Q × d) / 100
Where:
- μ is the dipole moment in debye (D)
- Q is the charge separation in statcoulomb (esu)
- d is the bond length in centimeters (cm)
Given that the dipole moment (μ) of HBr is 0.851 D and the percent ionic character is 12.6%, we can proceed with the calculation.
Step 1: Convert the dipole moment from debye (D) to the statcoulomb (esu).
1 D = 3.336 × 10^-29 esu
Dipole moment (μ) = 0.851 D = 0.851 × 3.336 × 10^-29 esu = 2.8328 × 10^-29 esu
Step 2: Calculate the charge separation (Q).
Q = (μ × 100) / d
Rearranging the equation:
d = (μ × 100) / Q
Given that the percent ionic character is 12.6%, the charge separation (Q) can be estimated as:
Q = 12.6% × 1.602 × 10^-19 C (Coulombs)
Step 3: Calculate the bond length (d) in centimeters (cm).
Convert picometers (pm) to centimeters (cm):
1 pm = 1 × 10^-10 cm
Finally, divide by 100 to convert from centimeters to picometers.
Let's proceed with the calculations:
Step 1: Convert the dipole moment to esu.
μ = 2.8328 × 10^-29 esu
Step 2: Calculate the charge separation (Q).
Q = 12.6% × 1.602 × 10^-19 C (Coulombs)
Q = 0.126 × 1.602 × 10^-19 C
Q = 2.02512 × 10^-20 C
Step 3: Calculate the bond length (d) in picometers (pm).
d = (μ × 100) / Q
d = (2.8328 × 10^-29 esu × 100) / (2.02512 × 10^-20 C)
d = 0.014 nn
Since 1 cm = 1 × 10^10 pm, we can convert from centimeters to picometers:
d = 0.014 cm × 1 × 10^10 pm/cm
d = 1.4 × 10^8 pm
Therefore, the estimated bond length of the H−Br bond in picometers is approximately 1.4 × 10^8 pm.