Now You Try

<p>The most intense earthquakes measured have had a value of about 8.9 on the Richter scale. How do these earthquakes compare in intensity to a standard, low-level earthquake?</p>

<p>Calculate the pH of a swimming pool with a hydrogen ion concentration of <code class='latex inline'>6.21\times 10^{-8} mol/L</code>.</p>

<p>Calculate the hydrogen ion concentration of each substance.</p>
<ul>
<li>baking soda, with a pH of 9</li>
</ul>

<p>How long will it take for $2500 to accumulate to $4000 if it is invested at an interest rate of 6.5%/a, compounded annually?</p>

<p>Calculate the hydrogen ion concentration of each substance.</p>
<ul>
<li>oven cleaner, with a pH of 13</li>
</ul>

<p>How many times as intense is the sound of a shout as the sound of a </p><p>a) conversation</p><p>b) whisper</p><p>when </p>
<ul>
<li>Intensity of shout = 80</li>
<li>Intensity of normal voice = 60</li>
<li>Intensity of whisper = 30</li>
</ul>

<p>The stellar magnitude scale compares the brightness of stars using the equation</p>
<ul>
<li><code class='latex inline'>
\displaystyle
m_2-m_1 = \log(\frac{b_1}{b_2})
</code></li>
</ul>
<p>where <code class='latex inline'>m_1</code> and <code class='latex inline'>m_2</code> are the apparent magnitudes of the two stars being compared (how bright they appear in the sky) and <code class='latex inline'>b_1</code> and <code class='latex inline'>b_2</code> are their brightness (how much light they actually emit). This relationship does not factor in how far from Earth the stars are.</p><p>(a) Sirius is the brightest-appearing star in our sky, with an apparent magnitude of <code class='latex inline'>-1.5</code>. How much brighter does Sirius appear than Betelgeuse, whose apparent magnitude is 0.12?</p><p>(b) The Sun appears about <code class='latex inline'>1.3 \times 10^{10}</code> times as brightly in our sky as does sirius. What is the apparent magnitude of the Sun?</p>

<p>If <code class='latex inline'>\log_{\sin x}(\cos x) = \frac{1}{2}</code>, and <code class='latex inline'>0 < x < \frac{\pi}{2}</code>, what is the value of <code class='latex inline'>\sin x</code>?</p>
<ul>
<li><strong>A.</strong> <code class='latex inline'>\frac{1}{\sqrt{3}}</code></li>
<li><strong>B.</strong> <code class='latex inline'>\frac{\sqrt{5}-1}{2}</code></li>
<li><strong>C.</strong> <code class='latex inline'>\frac{2}{\sqrt{3}}</code></li>
<li><strong>D.</strong> <code class='latex inline'>\frac{\sqrt{5} + 1}{3}</code></li>
<li><strong>E.</strong> <code class='latex inline'>\frac{2\sqrt{5} - 1}{2}</code></li>
</ul>

<p>Drinking water from a particular tap has a pH between 6.3 and 6.6. Is this tap water more or less acidic than distilled water? Explain your answer.</p>

<p>A new car has an interior sound level of 80dB at 50 km/h. A second car, at the same speed, has an interior sound level that is two times more intense than that of the new car. Calculate the sound level inside the second car.</p>

<p>Distilled water has an <code class='latex inline'>H^+</code> concentration of <code class='latex inline'>10^{-7} mol/L</code>. Calculate the pH of distilled water.</p>

<p>If <code class='latex inline'>\log_b(a^2) = 3</code>, which of the following is the value of <code class='latex inline'>\log_a(b^2)</code>?</p><p><code class='latex inline'>
\displaystyle
\begin{array}{cccccc}
&(A) & \frac{5}{3} &(B) & \frac{3}{4} &(C)& 2\frac{2}{3}
&(D) & \frac{4}{3} &(E) & \frac{3}{2} \\
\end{array}
</code></p>

<p>A triangle is contracted so that its base is a diagonal of a certain square and its area is equal to that of the square. Express the length of the altitude of the triangle in terms of the square's side length, <code class='latex inline'>s</code>.</p>

<p>On February 10, 2000, an earthquake happened in Welland, Ontario, that measured 2.3 on the Richter scale.</p><p>(a) How many times as intense was this as a standard low-level earthquake?</p><p>(b) On July 22, 2001, an earthquake in St. Catharines measured 1.1 on the Richter scale. How many times ass intense as the St. Catharines earthquake was the Welland earthquake?</p>

<p>Astronauts in space have just encountered three unknown stars and assigned them temporary names. Their absolute magnitude are recorded.</p><img src="/qimages/979" /><p> How much brighter, in absolute terms, is the brightest of these three stars than the </p>
<ul>
<li>i) second brightest?</li>
<li>ii) least brightest?</li>
</ul>

<p>The intensity, I, of light passing through water can be modelled by the equation <code class='latex inline'>I= 10^{1-0.13x}</code>, where <code class='latex inline'>x</code> is the depth of the water in metres. Most aquatic plants require a light intensity of 4.2 units for strong growth. Determine the depth of water at which most aquatic plants receive the required light.</p>

<p>The sound intensity of a pin drop is about <code class='latex inline'>\frac{1}{30000}</code> of the sound intensity of a normal conversation. What wish the decibel level of a pin drop?</p>

<p>Determine the pH of a solution with each hydronium ion concentration.</p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccccc}
&(a) &0.01 &(b)& 0.000 034 \\
&(c) & \log 10^{-9} &(d) & 1.5 \times 10^{-10} \\
\end{array}
</code></p>

<p>The sound level of a moving power lawn mower is 109 dB. The noise level in front of the amplifiers at a concert is about 118 dB. How many times louder is the noise at the front of the amplifiers than the noise of a moving power lawn mower?</p>

<p>On September 26, 2001, an earthquake in North Bay, Ontario, occurred that was 10 000 times as intense as <code class='latex inline'>I_0</code>. What was the measure of this earthquake on the Richter scale?</p>

<p>A wound, initially with an area of <code class='latex inline'>80 cm^2</code>, heals according to the formula <code class='latex inline'>A(t)= 80(10^{-0.023t})</code>, where <code class='latex inline'>A(t)</code> is the area of the wound in square centimetres after <code class='latex inline'>t</code> days of healing. In how many days will 75% of the wound be healed?</p>

<p>Determine the hydronium ion concentration, in moles per litre, of a solution with each pH.</p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccccc}
&(a) & 11 &(b)&3 \\
&(c) & 8.5 &(d) & 4.4 \\
\end{array}
</code></p>

<p>A particular sound is 1 000 000 times more intense than a sound you ca just barely hear. What is the loudness of the sound in decibels?</p>

<p>If one earthquake has a magnitude of 5.2 on the Richter scale and a second earthquake has a magnitude of 6, compare the intensities of the two earthquakes.</p>

<p>Calculate to two decimal places the pH of a solution with each concentration of <code class='latex inline'>H^+</code>.</p><p>(a) concentration of <code class='latex inline'>H^+ = 0.000 32</code></p><p>(b) concentration of <code class='latex inline'>H^+ = 0.000 3</code></p><p>(c) concentration of <code class='latex inline'>H^+ = 0. 000 045</code></p><p>(d) concentration of <code class='latex inline'>H^+ = 0.005</code></p>

<p>If <code class='latex inline'>a + b = 3</code> and <code class='latex inline'>a^2 + b^2 = 7</code>, then what is the value of <code class='latex inline'>a^4 + b^4</code>?</p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccc}
&(A) & 45 &(B)& 47 &(C) & 49
&(D) & 51 &(E)& 81\\
\end{array}
</code></p>

<p>How bright a star appears can depend on how much light the star actually emits and how far away it is. The stellar magnitude scale can be adjusted to account for distance as follows:</p>
<ul>
<li><code class='latex inline'>
\displaystyle
M_2-M_1 = \log(\frac{b_1}{b_2})
</code></li>
</ul>
<p>Here, M refers to a star's absolute magnitude, that is, how brightly it appears from a standard distance of 10 parsecs (or 32.6 light-years). The absolute brightness of Sirius is 1.4 and the absolute brightness of Betelgeuse is -8.1.</p><p>(a) Which of these two stars is brighter in absolute terms, and by how much?</p><p>(b) What does this suggest about these two starts' distance from Earth?</p>

<p>Determine the pH of a solution with a hydronimum ion concentration of </p><p><code class='latex inline'>
\displaystyle
\begin{array}{ccccccc}
&(a) & 0. 000 01 &(b)&2.5 \times 10^{11}\\
\end{array}
</code></p>

<p>A loud car stereo has a decibel level of <code class='latex inline'>110</code> dB. How many times as intense as the sound of a loud car stereo is the sound of a rock concert speaker?</p>
<ul>
<li>Intensity of shout = 80</li>
<li>Intensity of normal voice = 60</li>
<li>Intensity of whisper = 30</li>
<li>Intensity of car stereo = 110</li>
<li>Intensity of rock concert = 150</li>
</ul>

<p>Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning cycle. Every time the fluid is purified, 2.1% of it is lost. The fluid has to be topped up when half of the original build remains. After how many cycles will the fluid need to be topped up?</p>

<p>Calculate the hydrogen ion concentration of each substance.</p>
<ul>
<li>an egg, with a pH of 7.8</li>
</ul>

<p>Calculate the hydrogen ion concentration of each substance.</p>
<ul>
<li>milk, with a pH of 6.6</li>
</ul>

<p>The loudness of a heavy snore is 69 dB. How many times as loud as a normal conversation of 60 dB is a heavy snore?</p>

<p>The hydronium ion concentration of most chemicals varies from about <code class='latex inline'>10^{-15} mol/L</code> to <code class='latex inline'>0.1 mol/L</code>. Given this fact, why do you suppose that the pH scale was created </p><p>(a) in terms of a logarithmic function</p><p>(b) with a factor of <code class='latex inline'>-1</code></p>