Scientists use the pH scale to represent the level of acidity or alkalinity of a liquid. This is based on the molar concentration of hydrogen ions, [ H + ] . Since the values of [ H + ] vary over a large range, 1 × 10 0 mole per liter to 1 × 10 − 14 mole per liter mol/L , a logarithmic scale is used to compute pH . The formula pH = − log H + represents the pH of a liquid as a function of its concentration of hydrogen ions, [H + ] . The pH scale ranges from 0 to 14. Pure water is taken as neutral having a pH of 7. A pH less than 7 is acidic. A pH greater than 7 is alkaline (or basic). For Exercises 97-98, use the formula for pH . Round pH values to 1 decimal place. Bleach and milk of magnesia are both bases. Their H + values are 2.0 × 10 − 13 mol/L and 4.1 × 10 − 10 mol/L, respectively. a. Find the pH for bleach. b. Find the pH for milk of magnesia. c. Which substance is more basic?
Scientists use the pH scale to represent the level of acidity or alkalinity of a liquid. This is based on the molar concentration of hydrogen ions, [ H + ] . Since the values of [ H + ] vary over a large range, 1 × 10 0 mole per liter to 1 × 10 − 14 mole per liter mol/L , a logarithmic scale is used to compute pH . The formula pH = − log H + represents the pH of a liquid as a function of its concentration of hydrogen ions, [H + ] . The pH scale ranges from 0 to 14. Pure water is taken as neutral having a pH of 7. A pH less than 7 is acidic. A pH greater than 7 is alkaline (or basic). For Exercises 97-98, use the formula for pH . Round pH values to 1 decimal place. Bleach and milk of magnesia are both bases. Their H + values are 2.0 × 10 − 13 mol/L and 4.1 × 10 − 10 mol/L, respectively. a. Find the pH for bleach. b. Find the pH for milk of magnesia. c. Which substance is more basic?
Scientists use the
pH
scale to represent the level of acidity or alkalinity of a liquid. This is based on the molar concentration of hydrogen ions,
[
H
+
]
.
Since the values of
[
H
+
]
vary over a large range,
1
×
10
0
mole per liter to
1
×
10
−
14
mole per liter
mol/L
,
a logarithmic scale is used to compute
pH
.
The formula
pH
=
−
log
H
+
represents the pH of a liquid as a function of its concentration of hydrogen ions,
[H
+
]
.
The pH scale ranges from 0 to 14. Pure water is taken as neutral having a pH of 7. A pH less than 7 is acidic. A pH greater than 7 is alkaline (or basic). For Exercises 97-98, use the formula for
pH
.
Round
pH
values to 1 decimal place.
Bleach and milk of magnesia are both bases. Their
H
+
values are
2.0
×
10
−
13
mol/L and
4.1
×
10
−
10
mol/L,
respectively.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
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