Rate Law and ZnO (Zinc Oxide) in Sunscreen
- Page ID
- 418919
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Wearing sunscreen is the best and the easiest way to protect your skin. We are told over and over to wear it every day, 365 days of the year, rain or shine. What protects your skin from harmful UV rays is the active ingredient in the sunscreen, which is either chemical protection or mineral protection, such as zinc oxide.2
Figure 1: 3D structure of ZnO compound
Zinc oxide, or ZnO, is a common mineral protectant, a white, odorless solid, which reflects the sun’s light waves away from the skin.2 It effectively reflects light, is insoluble in water, and is photostable, making it the perfect compound to use in sunscreen.1 However, because ZnO is not water-soluble, it must be blended with a carrier agent so that it can be applied topically to the skin.5 ZnO-based sunscreen is highly recommended by dermatologists - patients who use zinc oxide sunscreen are less likely to develop skin cancer.4 Unlike many active ingredients used in sunscreen, zinc oxide is one of two UV type A sunscreen ingredients approved by the FDA.4 Some active ingredients in a particular sunscreen benefit certain types of skin, but zinc oxide is an effective sun protector for all skin types.5
Figure 2: The stereotypical look of active zinc oxide in sunscreen
Different brands of sunscreen have varying percentages of ZnO in their products. The percentage of ZnO in a container of sunscreen determines the sunscreen’s Sun Protection Factor or SPF. For every 1% of ZnO, a sample of sunscreen gains 1.6 SPF units.3 For example, sunscreens with less than 15% of ZnO have an SPF of 24 or less, while sunscreens with more than 20% of ZnO have at least 32 SPF. 3
Figure 3: Varying brands of ZnO sunscreens
Zinc oxide is a stable substance that does not break down easily in sunscreen, resulting in a long time for use.4 But like all substances, sunscreen decomposes, especially when on the skin. Rather than finding the SPF, the percentage of ZnO in the sunscreen is now used to predict the rate of decomposition by determining the mass of ZnO for every 100 mL of sunscreen. This molar mass translates ZnO from a particulate to a macroscopic concentration level. The rate of a particular sunscreen’s decomposition depends on this concentration of active ZnO in the sunscreen.2 Using the half-life of the active ZnO and the concentrations of ZnO in different sunscreens, we can predict its rate constant and the rate it will decompose when someone is wearing it. With a half-life of 0.64 hours,6 varying the concentration of the active ZnO in each sunscreen results in a certain life expectancy for the sunscreen.1
Key Equations:
ln[A]t = ln[A]0 - kt
k = ln(2)/t1/2
Rate = k[A]
A 3 fl. oz. container of “Umbra Sheer Physical Daily Defense” sunscreen contains 20% zinc oxide, ZnO. Find the rate for the decomposition of the zinc oxide in this sunscreen. The half-life of zinc oxide on someone's skin is 0.64 hours. The decomposition of zinc oxide is a first-order reaction.
Solution
We use the first-order integrated form of the rate law.
ln[ZnO]t = ln[ZnO]0 - kt
There are 4 variables in the integrated rate law. We use t and the relative concentration of [ZnO]0 and [ZnO]t to find k. Because t1/2 is provided, we do not need to solve for a numerical concentration of [ZnO]0 or [ZnO]t. At the half-life time, half of the original concentration of ZnO has been decomposed.
ln[ZnO]0/2 = ln[ZnO]0 - kt1/2
The equation is rearranged to isolate k and the concentration of ZnO cancels. Half-life must be converted to seconds for correct units.
k = ln(2)/t1/2
k = (ln(2)/.64 hr )( 1 hr / 3600 s)
k = 3.008 x 10-4 /s
The k value is then substituted into the first-order rate law to find the reaction rate of ZnO decomposition. Convert grams of ZnO as a percentage of milliliters to molarity.
20.0 g ZnO /100 mL sunscreen = 2 g ZnO / 1 L sunscreen ( 1 mol ZnO/ 81.38 g) = 0.025 M ZnO
Rate = k[ZnO]
Rate = (3.008 x 10-4 /s )(0.025 M ZnO)
Rate = 7.521 x 10-6 M/s
The greater the concentration of the ZnO in your sunscreen, the greater the rate of decomposition. With a greater SPF, the sunscreen will protect your skin from the sun for a longer period of time.
How much ZnO will be left after being on someone’s skin for 1.5 hours?
Solution
First, convert hours to seconds.
(1.5 hour)(3600 s/ 1 hour) = 5400 s
There are 4 variables in the integrated rate law. We use t, k, and the initial concentration of [ZnO]0 to find [ZnO]t, the concentration of ZnO at 1 hour.
ln[ZnO]t = ln[ZnO]0 - kt
ln[ZnO]t = ln[0.025] - (3.008 x 10-4 /s)(5400 s)
ln[ZnO]t = -5.313
[ZnO]t = 4.925 x 10-3
After 1.5 hours, the concentration of active ZnO in the sunscreen on someone’s skin has decreased from 0.025 M to 0.00495 M. This is 19.7% of the original concentration of sunscreen that was originally on the skin. With this little ZnO, the skin is unprotected.
ZnO in sunscreen decomposes readily when it is spread on the skin. Before long, nothing is protecting your skin, leaving it at risk for major permanent damage and cancer. Make sure to apply your sunscreen regularly.
References:
1: Zinc Oxide, https://pubchem.ncbi.nlm.nih.gov/compound/Zinc-oxide (accessed Nov.8, 2022).
2: Rud, M. The 14 Best Zinc Oxide Sunscreens of 2022, https://www.byrdie.com/best-zinc-oxi...creens-4687640 (accessed Nov.8, 2022).
3: Zickerman, T. All Mineral Sunscreens are Not Created Equal - Low Concentrations .. https://lovesunbody.com/blogs/news/a...uvb-protection (accessed Nov.8, 2022).
4: Bailey, C. Are zinc oxide sunscreens better? https://drbaileyskincare.com/blogs/b...screens-better (accessed Nov 8, 2022).
5: Everything you want to know about zinc oxide. https://projectsunscreen.com/blogs/n...out-zinc-oxide (accessed Nov 8, 2022).
6: Zainul, R. Determination of the half-life and the quantum yield of ZnO semiconductor photocatalyst in humic acid. https://www.researchgate.net/publica..._in_humic_acid (accessed Nov 30, 2022)
Figure:
Figure 1: https://materialsproject.org/materia...p-2133#summary
Figure 2 https://www.ocregister.com/2013/05/2...ather-on-zinc/
Figure 3: https://malaysia.news.yahoo.com/13-z...n9gsHs-090Mhwi