Effect of sample size on Chi-squared distribution As the degrees of freedom increase, the chi-square curve approaches a normal distribution. But what about increasing the sample size?
If I am using degree of freedom =1, but with different sample sizes (eg n=10, 30 and 50), will the chi-square curve become more normal with increasing sample size?

One of the best ways to understand statistical concepts is just to simulate the random experiments yourself. Here is some R code which illustrates what happens as you increase the sample size.
simulate = function(n){
  data = rpois(n, lambda = 1)
  Obs.0 = sum(data == 0)
  Obs.1 = sum(data == 1)
  Obs.2 = sum(data >= 2)
  Exp.0 = dpois(0, lambda = 1)*n
  Exp.1 = dpois(1, lambda = 1)*n
  Exp.2 = n - (Exp.0 + Exp.1)
  chi = 0
  chi = chi + (Obs.0-Exp.0)^2/Exp.0
  chi = chi + (Obs.1-Exp.1)^2/Exp.1
  chi = chi + (Obs.2-Exp.2)^2/Exp.2
  chi
}

result = replicate(1e2, simulate(1e2))
plot(density(result))
curve(dchisq(x,2), add=TRUE, col="red")

Let us explain what this code does. When you run simulate(n), the computer generates $n$ (independent) random samples from Poisson(1). We created three categories, whose where the sample = 0, those were sample = 1, and those were sample >= 2. We calculate the expected count vs the actual count. In the end the chi-squared statistic is calculated for that data set.
But this is just 1 number. So now we replicate this process $10^2$ times. Generating $10^2$ different values of the chi-squared statistic. Then we tell the computer to draw the estimate distribution function for all those chi-squared values. Finally, the idealized chi-squared distribution is drawn in red.
Notice, if you increase the replication number from $10^2$ slowly up to $10^5$, the fit gets closer to the idealized chi-squared.
