Table of Contents
Is ln of a number dimensionless?
The real deal is that you cannot take the log (or ln) of a number that actually has units, i.e., before the log (or ln) is applied, the unit must be dimensionless. You may be familiar with the concept of making quantities that otherwise have units, unitless, as being referred to as activities in chemistry.
What is the dimension of natural logarithm?
The natural logarithm lnX is defined as the area under the curve y=1/x y = 1 / x from x=1 to X : lnX≡∫Xx=1dxx. (1) This integral is the sum of an infinite number of terms “dx/x d x / x “, each of which is dimensionless.
What are the dimensions of logarithm?
“The Dimensions of Logarithmic Quantities” f J. Chem. of quantities that are not dimensionless. Thus d log (x) is always dimensionless, like A log (x), whether or not x is dimensionless.
Does the ln of something have units?
Overall, the argument x of ln(x) must be unitless, and a log transformed quantity must be unitless. If x=0.5 is measured in some units, say, seconds, then taking the log actually means ln(0.5s/1s)=ln(0.5). See this for more information about other transcendental functions.
What are the units for ln k?
When people write lnk, what they usually mean is ln(k/k∘) where k∘ has the numerical value of 1 and the units of whatever k is in. Once you have the y-intercept, you take the exponential of that and tack the units back on to get A.
What are the units of ln concentration?
The units of a ln(p) would generally be referred to as “log Pa” or “log atm.” Taking the logarithm doesn’t actually change the dimension of the argument at all — the logarithm of pressure is still pressure — but it does change the numerical value, and thus “Pa” and “log Pa” should be considered different units.
What is the dimension of exponential function?
the graph of the exponential function is a two-dimensional surface curving through four dimensions.
Do logarithms change units?
11 Answers. Yes, logarithms always give dimensionless numbers, but no, it’s not physical to take the logarithm of anything with units.
What is K in ln k?
When the lnk (rate constant) is plotted versus the inverse of the temperature (kelvin), the slope is a straight line. The value of the slope (m) is equal to -Ea/R where R is a constant equal to 8.314 J/mol-K….
| T (K) | k (s-1) |
|---|---|
| 318 | 2.51 x 10-4 |
| 328 | 7.59 x 10-4 |
| 338 | 2.40 x 10-3 |