- In terms of hydrogen ion concentration, how much more acidic is Solution A, with a pH of 1.6, than Solution with a pH of 2.5? Round your answer to the nearest 10th???? 2. Early in the century the earthquake in San Francisco registered 8.3 on the Richter scale. In the same year, and earthquake was recorded in South America that was four time stronger. What was the magnitude of the earthquake in South American????? 3. A gunshot is about 2.5 x
times as intense as threshold sound and has a decibel rating of about 134 dB. T decibel rating of a cat’s purr is about 25 dB. How many more times intense is the sound of a gunshot than a purr?????
The Correct Answer and Explanation is:
Let’s break down each question:
1. In terms of hydrogen ion concentration, how much more acidic is Solution A (pH = 1.6) than Solution with a pH of 2.5?
The pH scale is logarithmic, meaning each unit change in pH represents a 10-fold change in hydrogen ion concentration.
The formula for hydrogen ion concentration (in molarity, [H+]) from pH is:[H+]=10−pH[H^+] = 10^{-\text{pH}}[H+]=10−pH
- For Solution A (pH = 1.6): [H+]A=10−1.6≈2.51×10−2 M[H^+]_A = 10^{-1.6} \approx 2.51 \times 10^{-2} \, \text{M}[H+]A=10−1.6≈2.51×10−2M
- For Solution B (pH = 2.5): [H+]B=10−2.5≈3.16×10−3 M[H^+]_B = 10^{-2.5} \approx 3.16 \times 10^{-3} \, \text{M}[H+]B=10−2.5≈3.16×10−3M
To find how many times more acidic Solution A is compared to Solution B, we take the ratio of the hydrogen ion concentrations:[H+]A[H+]B=2.51×10−23.16×10−3≈7.95\frac{[H^+]_A}{[H^+]_B} = \frac{2.51 \times 10^{-2}}{3.16 \times 10^{-3}} \approx 7.95[H+]B[H+]A=3.16×10−32.51×10−2≈7.95
So, Solution A is about 8 times more acidic than Solution B.
2. What was the magnitude of the earthquake in South America, given that it was four times stronger than the San Francisco earthquake with a magnitude of 8.3?
The Richter scale is logarithmic, meaning each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 32 times more energy release. The formula to calculate the magnitude difference is:Magnitude difference=log10(I2/I1)\text{Magnitude difference} = \log_{10}(I_2 / I_1)Magnitude difference=log10(I2/I1)
Where I2I_2I2 is the intensity of the South American earthquake and I1I_1I1 is the intensity of the San Francisco earthquake. Since the South American earthquake was 4 times stronger, the intensity ratio is 4.log10(4)≈0.602\log_{10}(4) \approx 0.602log10(4)≈0.602
Now, to find the magnitude of the South American earthquake:Magnitude of South American earthquake=8.3+0.602≈8.9\text{Magnitude of South American earthquake} = 8.3 + 0.602 \approx 8.9Magnitude of South American earthquake=8.3+0.602≈8.9
So, the magnitude of the South American earthquake was approximately 8.9.
3. How many more times intense is the sound of a gunshot than a cat’s purr?
The decibel (dB) scale is logarithmic as well. The formula for the intensity level in decibels is:dB=10log10(II0)\text{dB} = 10 \log_{10} \left( \frac{I}{I_0} \right)dB=10log10(I0I)
Where III is the sound intensity and I0I_0I0 is the reference intensity (threshold of hearing). The difference in dB levels between two sounds can be used to calculate how many times more intense one sound is than the other:ΔdB=10log10(I2I1)\Delta \text{dB} = 10 \log_{10} \left( \frac{I_2}{I_1} \right)ΔdB=10log10(I1I2)
Given that the gunshot is about 134 dB and the cat’s purr is about 25 dB, we can calculate the difference in dB:ΔdB=134−25=109 dB\Delta \text{dB} = 134 – 25 = 109 \, \text{dB}ΔdB=134−25=109dB
Now, using the formula to find the intensity ratio:109=10log10(IgunshotIpurr)109 = 10 \log_{10} \left( \frac{I_{\text{gunshot}}}{I_{\text{purr}}} \right)109=10log10(IpurrIgunshot)IgunshotIpurr=1010910=1010.9≈7.94×1010\frac{I_{\text{gunshot}}}{I_{\text{purr}}} = 10^{\frac{109}{10}} = 10^{10.9} \approx 7.94 \times 10^{10}IpurrIgunshot=1010109=1010.9≈7.94×1010
So, the sound of the gunshot is approximately 79 billion times more intense than the cat’s purr.
Summary of Answers:
- Solution A is 8 times more acidic than Solution B.
- The South American earthquake had a magnitude of 8.9.
- The sound of the gunshot is about 79 billion times more intense than the cat’s purr.
